<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2023 Workiva-->
<!--r:4d97f989-049f-496e-8b5f-e1f82b4d6d0a,g:83cbf50a-84dd-43e5-818d-2dcd09dd3f05-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://composecure.com/role/ConsolidatedBalanceSheets" xlink:type="simple" xlink:href="cmpo-20230930.xsd#ConsolidatedBalanceSheets"/>
  <link:calculationLink xlink:role="http://composecure.com/role/ConsolidatedBalanceSheets" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_cb3ce592-c0dd-4bca-a824-1e978be9f84c" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue_17e63178-273b-42fd-8bff-f0cdf496ca3f" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockValue"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_cb3ce592-c0dd-4bca-a824-1e978be9f84c" xlink:to="loc_us-gaap_CommonStockValue_17e63178-273b-42fd-8bff-f0cdf496ca3f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_b4c44a0f-4d39-475f-9493-f7c5965d0b99" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_cb3ce592-c0dd-4bca-a824-1e978be9f84c" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_b4c44a0f-4d39-475f-9493-f7c5965d0b99" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital_692c0cb0-cbbf-4cd9-9626-3db962ad11ed" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_cb3ce592-c0dd-4bca-a824-1e978be9f84c" xlink:to="loc_us-gaap_AdditionalPaidInCapital_692c0cb0-cbbf-4cd9-9626-3db962ad11ed" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit_b37fdab1-752d-4fbc-a8ad-80d237e52570" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_cb3ce592-c0dd-4bca-a824-1e978be9f84c" xlink:to="loc_us-gaap_RetainedEarningsAccumulatedDeficit_b37fdab1-752d-4fbc-a8ad-80d237e52570" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue_c30d33d7-a041-4980-b57a-af178b0e5301" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockValue"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_cb3ce592-c0dd-4bca-a824-1e978be9f84c" xlink:to="loc_us-gaap_PreferredStockValue_c30d33d7-a041-4980-b57a-af178b0e5301" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent_bf6a7ab3-405a-4a14-9039-f0155f0e2322" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:to="loc_us-gaap_LongTermDebtCurrent_bf6a7ab3-405a-4a14-9039-f0155f0e2322" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_CommissionPayableCurrent_68d9d3c9-3632-4635-bbe7-b0b95af969a9" xlink:href="cmpo-20230930.xsd#cmpo_CommissionPayableCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:to="loc_cmpo_CommissionPayableCurrent_68d9d3c9-3632-4635-bbe7-b0b95af969a9" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedBonusesCurrent_79b4b9e3-37a6-4764-9191-3f85b6fe31bf" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedBonusesCurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:to="loc_us-gaap_AccruedBonusesCurrent_79b4b9e3-37a6-4764-9191-3f85b6fe31bf" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent_d6fd535a-cbb5-4637-b26f-1edb4929f1b1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:to="loc_us-gaap_AccountsPayableCurrent_d6fd535a-cbb5-4637-b26f-1edb4929f1b1" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent_6c0471f4-f76c-4c9a-a58e-18fc7b47f483" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:to="loc_us-gaap_AccruedLiabilitiesCurrent_6c0471f4-f76c-4c9a-a58e-18fc7b47f483" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent_9333884a-073d-4a56-98c9-12a3609f098c" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:to="loc_us-gaap_OperatingLeaseLiabilityCurrent_9333884a-073d-4a56-98c9-12a3609f098c" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityCurrent_f2a07c0c-e523-4aa2-8248-28c8d7eee174" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityCurrent"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_257bc7a1-0e44-4e96-8bfd-db1df1a551de" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityCurrent_f2a07c0c-e523-4aa2-8248-28c8d7eee174" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets_57c0dd81-c24b-41c8-bd63-7f8cc41e9b4f" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Assets"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_DepositsAndOtherAssetsNoncurrent_aa6ae40a-0ff9-4eb3-99fe-f2f5674a5d6f" xlink:href="cmpo-20230930.xsd#cmpo_DepositsAndOtherAssetsNoncurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_57c0dd81-c24b-41c8-bd63-7f8cc41e9b4f" xlink:to="loc_cmpo_DepositsAndOtherAssetsNoncurrent_aa6ae40a-0ff9-4eb3-99fe-f2f5674a5d6f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsNoncurrent_b66dc869-253d-412c-b193-109fc7533fd4" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetsNoncurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_57c0dd81-c24b-41c8-bd63-7f8cc41e9b4f" xlink:to="loc_us-gaap_DerivativeAssetsNoncurrent_b66dc869-253d-412c-b193-109fc7533fd4" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet_137645a9-123e-4d0e-8136-10439d579632" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_57c0dd81-c24b-41c8-bd63-7f8cc41e9b4f" xlink:to="loc_us-gaap_DeferredIncomeTaxAssetsNet_137645a9-123e-4d0e-8136-10439d579632" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_2af37a25-fb81-4214-b4dc-060b816aa924" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsCurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_57c0dd81-c24b-41c8-bd63-7f8cc41e9b4f" xlink:to="loc_us-gaap_AssetsCurrent_2af37a25-fb81-4214-b4dc-060b816aa924" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet_43e3ae9d-86a8-40ae-bd65-fe591c61e989" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_57c0dd81-c24b-41c8-bd63-7f8cc41e9b4f" xlink:to="loc_us-gaap_PropertyPlantAndEquipmentNet_43e3ae9d-86a8-40ae-bd65-fe591c61e989" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset_72d9f818-60ae-4bde-b0ca-af882061385d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_57c0dd81-c24b-41c8-bd63-7f8cc41e9b4f" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAsset_72d9f818-60ae-4bde-b0ca-af882061385d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Liabilities"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityNoncurrent_54984f7a-38ff-4cdc-9761-ccf6056ef177" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityNoncurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityNoncurrent_54984f7a-38ff-4cdc-9761-ccf6056ef177" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_edc079f2-f28a-4792-b0ff-c2f7ce8f3f15" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_edc079f2-f28a-4792-b0ff-c2f7ce8f3f15" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_dc0c8de7-5a50-4187-9a5e-162c8557afae" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_dc0c8de7-5a50-4187-9a5e-162c8557afae" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLongTermDebtNoncurrent_598f95fa-fc28-4a4d-b8dd-c1495d719c0f" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLongTermDebtNoncurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_us-gaap_OtherLongTermDebtNoncurrent_598f95fa-fc28-4a4d-b8dd-c1495d719c0f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstanding_677c8590-6032-4240-8059-f702b2476b73" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WarrantsAndRightsOutstanding"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_us-gaap_WarrantsAndRightsOutstanding_677c8590-6032-4240-8059-f702b2476b73" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_DerivativeInstrumentContingentConsiderationLiability_2efc939e-75cb-47e1-be8e-86719edbf0ff" xlink:href="cmpo-20230930.xsd#cmpo_DerivativeInstrumentContingentConsiderationLiability"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_cmpo_DerivativeInstrumentContingentConsiderationLiability_2efc939e-75cb-47e1-be8e-86719edbf0ff" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent_6e4d50ef-fa6c-4b8a-b787-1b8ec47ab248" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_us-gaap_LiabilitiesCurrent_6e4d50ef-fa6c-4b8a-b787-1b8ec47ab248" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertibleLongTermNotesPayable_668d3aa2-c0e4-4971-bab8-e27675aa0022" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ConvertibleLongTermNotesPayable"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_65d83876-1b2b-462f-9d7d-63886a2d9e5c" xlink:to="loc_us-gaap_ConvertibleLongTermNotesPayable_668d3aa2-c0e4-4971-bab8-e27675aa0022" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity_d799677a-d283-4208-b25b-bb326469f15a" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_f4977b5b-c8a5-45f4-81a4-eb7c2ff4197d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquity"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_d799677a-d283-4208-b25b-bb326469f15a" xlink:to="loc_us-gaap_StockholdersEquity_f4977b5b-c8a5-45f4-81a4-eb7c2ff4197d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_1c285576-c420-4f15-8e16-fd72486970b5" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Liabilities"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_d799677a-d283-4208-b25b-bb326469f15a" xlink:to="loc_us-gaap_Liabilities_1c285576-c420-4f15-8e16-fd72486970b5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_42a48b6c-40bb-4093-85a5-7217146e15c5" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_d799677a-d283-4208-b25b-bb326469f15a" xlink:to="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_42a48b6c-40bb-4093-85a5-7217146e15c5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies_60ae82b7-0970-4379-89de-aae0247e6d54" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_d799677a-d283-4208-b25b-bb326469f15a" xlink:to="loc_us-gaap_CommitmentsAndContingencies_60ae82b7-0970-4379-89de-aae0247e6d54" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_09aa73f4-0d0b-44fa-a05e-8bd76424e49b" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_3397ec9b-9557-455c-b05b-23887f160023" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_09aa73f4-0d0b-44fa-a05e-8bd76424e49b" xlink:to="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_3397ec9b-9557-455c-b05b-23887f160023" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent_b420b7ce-8571-4cf5-9efd-9c6321c0f827" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_09aa73f4-0d0b-44fa-a05e-8bd76424e49b" xlink:to="loc_us-gaap_AccountsReceivableNetCurrent_b420b7ce-8571-4cf5-9efd-9c6321c0f827" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_d7867d90-ea49-4044-ad41-abbe65f5bfd3" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_09aa73f4-0d0b-44fa-a05e-8bd76424e49b" xlink:to="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_d7867d90-ea49-4044-ad41-abbe65f5bfd3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet_3a2577f9-df31-4db1-832b-a1a7790e6f11" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryNet"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_09aa73f4-0d0b-44fa-a05e-8bd76424e49b" xlink:to="loc_us-gaap_InventoryNet_3a2577f9-df31-4db1-832b-a1a7790e6f11" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/ConsolidatedStatementsofOperationsUnaudited" xlink:type="simple" xlink:href="cmpo-20230930.xsd#ConsolidatedStatementsofOperationsUnaudited"/>
  <link:calculationLink xlink:role="http://composecure.com/role/ConsolidatedStatementsofOperationsUnaudited" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss_ceeb9827-5978-4020-8d32-f47ec616a7f7" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense_134d80c5-8083-43be-b540-34a8894d3095" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingIncomeLoss_ceeb9827-5978-4020-8d32-f47ec616a7f7" xlink:to="loc_us-gaap_GeneralAndAdministrativeExpense_134d80c5-8083-43be-b540-34a8894d3095" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit_a00b7c6d-f135-4b55-a238-f9c8374db5b6" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GrossProfit"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingIncomeLoss_ceeb9827-5978-4020-8d32-f47ec616a7f7" xlink:to="loc_us-gaap_GrossProfit_a00b7c6d-f135-4b55-a238-f9c8374db5b6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_6ed1dcd3-6391-4c20-b6ec-6ba7d067877b" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProfitLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit_64725963-836a-412d-a335-8a3bff1c5a98" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_ProfitLoss_6ed1dcd3-6391-4c20-b6ec-6ba7d067877b" xlink:to="loc_us-gaap_IncomeTaxExpenseBenefit_64725963-836a-412d-a335-8a3bff1c5a98" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_1605f554-5240-4ef2-8136-62152f5d6ac6" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_ProfitLoss_6ed1dcd3-6391-4c20-b6ec-6ba7d067877b" xlink:to="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_1605f554-5240-4ef2-8136-62152f5d6ac6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_44fc39d8-1df5-474c-82d1-276eb2bb0fb7" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss_fe22149c-5267-400b-9461-14f327215891" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_44fc39d8-1df5-474c-82d1-276eb2bb0fb7" xlink:to="loc_us-gaap_OperatingIncomeLoss_fe22149c-5267-400b-9461-14f327215891" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense_b26c63c5-9e48-4172-a0dd-845a7fa55263" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_44fc39d8-1df5-474c-82d1-276eb2bb0fb7" xlink:to="loc_us-gaap_NonoperatingIncomeExpense_b26c63c5-9e48-4172-a0dd-845a7fa55263" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss_81b98702-d19e-416c-b3c0-e633fddf0ece" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_e110ee6a-e293-4a5f-ad6b-9a8d5dd8209e" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLoss_81b98702-d19e-416c-b3c0-e633fddf0ece" xlink:to="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_e110ee6a-e293-4a5f-ad6b-9a8d5dd8209e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_9c4fd4b9-26a7-4c7d-ac44-30f16e5eda79" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLoss_81b98702-d19e-416c-b3c0-e633fddf0ece" xlink:to="loc_us-gaap_ProfitLoss_9c4fd4b9-26a7-4c7d-ac44-30f16e5eda79" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense_2e51b368-c13f-4ff0-96bc-2de63eebb1b0" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_DerivativeInstrumentChangeInAmountOfContingentConsiderationLiability_89175593-79e9-43c5-95ad-16f64c73a77a" xlink:href="cmpo-20230930.xsd#cmpo_DerivativeInstrumentChangeInAmountOfContingentConsiderationLiability"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_2e51b368-c13f-4ff0-96bc-2de63eebb1b0" xlink:to="loc_cmpo_DerivativeInstrumentChangeInAmountOfContingentConsiderationLiability_89175593-79e9-43c5-95ad-16f64c73a77a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNonoperatingNet_f1d07631-2665-41b3-bf77-be2e7e4fcfd3" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestIncomeExpenseNonoperatingNet"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_2e51b368-c13f-4ff0-96bc-2de63eebb1b0" xlink:to="loc_us-gaap_InterestIncomeExpenseNonoperatingNet_f1d07631-2665-41b3-bf77-be2e7e4fcfd3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAdjustmentOfWarrants_996b74af-2874-4a95-8d5d-42389ef2bd60" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAdjustmentOfWarrants"/>
    <link:calculationArc order="3" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_2e51b368-c13f-4ff0-96bc-2de63eebb1b0" xlink:to="loc_us-gaap_FairValueAdjustmentOfWarrants_996b74af-2874-4a95-8d5d-42389ef2bd60" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmbeddedDerivativeGainLossOnEmbeddedDerivativeNet_4adb148b-3a95-4ae2-a3ba-ecc04a1b0485" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmbeddedDerivativeGainLossOnEmbeddedDerivativeNet"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_2e51b368-c13f-4ff0-96bc-2de63eebb1b0" xlink:to="loc_us-gaap_EmbeddedDerivativeGainLossOnEmbeddedDerivativeNet_4adb148b-3a95-4ae2-a3ba-ecc04a1b0485" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_AmortizationOfDebtIssuanceCostsAndOtherFees_5c54c059-988f-4f4c-bfd2-0309b4116e17" xlink:href="cmpo-20230930.xsd#cmpo_AmortizationOfDebtIssuanceCostsAndOtherFees"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_2e51b368-c13f-4ff0-96bc-2de63eebb1b0" xlink:to="loc_cmpo_AmortizationOfDebtIssuanceCostsAndOtherFees_5c54c059-988f-4f4c-bfd2-0309b4116e17" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense_e5e046ad-1fd4-47f7-9a25-859e021cd2ad" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_2e51b368-c13f-4ff0-96bc-2de63eebb1b0" xlink:to="loc_us-gaap_OtherNonoperatingIncomeExpense_e5e046ad-1fd4-47f7-9a25-859e021cd2ad" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit_c77f9f68-559b-4519-9ec1-c7694093675d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GrossProfit"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_e2e9d69a-6101-44ae-ae28-4f60aca38b20" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_GrossProfit_c77f9f68-559b-4519-9ec1-c7694093675d" xlink:to="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_e2e9d69a-6101-44ae-ae28-4f60aca38b20" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold_a59bf3d7-f406-485d-b1cd-b0b7de9a054b" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_GrossProfit_c77f9f68-559b-4519-9ec1-c7694093675d" xlink:to="loc_us-gaap_CostOfGoodsAndServicesSold_a59bf3d7-f406-485d-b1cd-b0b7de9a054b" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/ConsolidatedStatementsofComprehensiveIncomeUnaudited" xlink:type="simple" xlink:href="cmpo-20230930.xsd#ConsolidatedStatementsofComprehensiveIncomeUnaudited"/>
  <link:calculationLink xlink:role="http://composecure.com/role/ConsolidatedStatementsofComprehensiveIncomeUnaudited" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_87a44a65-7f81-4e0d-9291-2651e5816a73" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax_fdd5fd1d-9105-4922-b427-3d2fe25620c5" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_87a44a65-7f81-4e0d-9291-2651e5816a73" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax_fdd5fd1d-9105-4922-b427-3d2fe25620c5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_9b859080-a105-48bc-83db-666b7b9415e6" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_d5f94119-2f7d-4e71-9939-929c69e78360" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_9b859080-a105-48bc-83db-666b7b9415e6" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_d5f94119-2f7d-4e71-9939-929c69e78360" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_6de99afe-17e9-4e06-ac2e-84d00bab1234" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_9b859080-a105-48bc-83db-666b7b9415e6" xlink:to="loc_us-gaap_ProfitLoss_6de99afe-17e9-4e06-ac2e-84d00bab1234" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/ConsolidatedStatementsofCashFlowsUnaudited" xlink:type="simple" xlink:href="cmpo-20230930.xsd#ConsolidatedStatementsofCashFlowsUnaudited"/>
  <link:calculationLink xlink:role="http://composecure.com/role/ConsolidatedStatementsofCashFlowsUnaudited" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_5714f822-57a5-414d-b7a1-7cb0db95d655" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_3b8b4874-48e7-48e9-b89b-552ec530b4f8" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_5714f822-57a5-414d-b7a1-7cb0db95d655" xlink:to="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_3b8b4874-48e7-48e9-b89b-552ec530b4f8" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfSecuredDebt_0238d33c-4603-4be1-94ea-90c36b54477e" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RepaymentsOfSecuredDebt"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_us-gaap_RepaymentsOfSecuredDebt_0238d33c-4603-4be1-94ea-90c36b54477e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_PaymentOfDistributionsToNoncontrollingInterests_9b327b51-8f3b-40f7-9901-277c86f9589e" xlink:href="cmpo-20230930.xsd#cmpo_PaymentOfDistributionsToNoncontrollingInterests"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_cmpo_PaymentOfDistributionsToNoncontrollingInterests_9b327b51-8f3b-40f7-9901-277c86f9589e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_f00c9f6d-32b8-4397-ac09-2b07edc8497e" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_f00c9f6d-32b8-4397-ac09-2b07edc8497e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts_6acb7026-51ef-44a3-9bc1-f048dfa4b1b3" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:calculationArc order="4" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_us-gaap_PaymentsOfDebtIssuanceCosts_6acb7026-51ef-44a3-9bc1-f048dfa4b1b3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLinesOfCredit_3f0782e4-fcc9-4f6b-ac68-ab2411200e21" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RepaymentsOfLinesOfCredit"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_us-gaap_RepaymentsOfLinesOfCredit_3f0782e4-fcc9-4f6b-ac68-ab2411200e21" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_13fb144d-c954-4074-a292-45cf428ca854" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:calculationArc order="6" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_13fb144d-c954-4074-a292-45cf428ca854" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_PaymentOfIssuanceCostsRecapitalization_d29b7978-24ad-43dd-b70a-8e428c83a3a6" xlink:href="cmpo-20230930.xsd#cmpo_PaymentOfIssuanceCostsRecapitalization"/>
    <link:calculationArc order="7" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_cmpo_PaymentOfIssuanceCostsRecapitalization_d29b7978-24ad-43dd-b70a-8e428c83a3a6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_PaymentOnTaxReceivableAgreementLiability_4b8a213f-d8aa-4db0-ad53-da4a88a4e3cd" xlink:href="cmpo-20230930.xsd#cmpo_PaymentOnTaxReceivableAgreementLiability"/>
    <link:calculationArc order="8" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_d32ebb51-dd59-4082-bdab-e4a5ae84f4e1" xlink:to="loc_cmpo_PaymentOnTaxReceivableAgreementLiability_4b8a213f-d8aa-4db0-ad53-da4a88a4e3cd" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_60cee364-0a3e-45cf-abcd-312231e07636" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_ProfitLoss_60cee364-0a3e-45cf-abcd-312231e07636" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayable_3d60520f-fa27-4fdb-8657-dc9fea9fb15b" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_IncreaseDecreaseInAccountsPayable_3d60520f-fa27-4fdb-8657-dc9fea9fb15b" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_DerivativeInstrumentChangeInAmountOfContingentConsiderationLiability_9e6c978c-4c80-4d66-b4f5-0108ac033045" xlink:href="cmpo-20230930.xsd#cmpo_DerivativeInstrumentChangeInAmountOfContingentConsiderationLiability"/>
    <link:calculationArc order="3" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_cmpo_DerivativeInstrumentChangeInAmountOfContingentConsiderationLiability_9e6c978c-4c80-4d66-b4f5-0108ac033045" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAdjustmentOfWarrants_1f2064d2-f765-46e7-a20b-6885ac815863" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAdjustmentOfWarrants"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_FairValueAdjustmentOfWarrants_1f2064d2-f765-46e7-a20b-6885ac815863" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInventories_0f8bde76-b3f8-47a3-b22f-9ebe37a2f6c0" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInInventories"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_IncreaseDecreaseInInventories_0f8bde76-b3f8-47a3-b22f-9ebe37a2f6c0" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_e7b7adf3-efc0-4279-a38d-beaf7aef4054" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:calculationArc order="6" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_e7b7adf3-efc0-4279-a38d-beaf7aef4054" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmbeddedDerivativeGainLossOnEmbeddedDerivativeNet_7c2cd40a-d39e-45ea-8fcb-872fb2790202" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmbeddedDerivativeGainLossOnEmbeddedDerivativeNet"/>
    <link:calculationArc order="7" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_EmbeddedDerivativeGainLossOnEmbeddedDerivativeNet_7c2cd40a-d39e-45ea-8fcb-872fb2790202" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts_b6035762-a6be-4a02-94ea-64e5c196d4fa" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_AmortizationOfFinancingCosts_b6035762-a6be-4a02-94ea-64e5c196d4fa" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable_19036c9b-e728-4efa-bcad-b8f2ac2f6b8a" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:calculationArc order="9" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_IncreaseDecreaseInAccountsReceivable_19036c9b-e728-4efa-bcad-b8f2ac2f6b8a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities_78dac9d7-d9cd-4631-8ed1-2fe34a777ce2" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <link:calculationArc order="10" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities_78dac9d7-d9cd-4631-8ed1-2fe34a777ce2" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_b7613117-e2d2-4e17-8a18-0e45f9385d38" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
    <link:calculationArc order="11" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_b7613117-e2d2-4e17-8a18-0e45f9385d38" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_IncreaseDecreaseInDepositAndOtherAssets_f4908a3e-7a50-4eed-9171-2ae0be648a52" xlink:href="cmpo-20230930.xsd#cmpo_IncreaseDecreaseInDepositAndOtherAssets"/>
    <link:calculationArc order="12" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_cmpo_IncreaseDecreaseInDepositAndOtherAssets_f4908a3e-7a50-4eed-9171-2ae0be648a52" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit_2c81b4e6-565c-4d65-87e1-79f64570e1d9" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:calculationArc order="13" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_DeferredIncomeTaxExpenseBenefit_2c81b4e6-565c-4d65-87e1-79f64570e1d9" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation_800e7efd-0e6c-4bf5-aed5-0d4cd2bcea23" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensation"/>
    <link:calculationArc order="14" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_ShareBasedCompensation_800e7efd-0e6c-4bf5-aed5-0d4cd2bcea23" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization_b34bc44f-9eea-44b1-8108-d7c7f6006ab3" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:calculationArc order="15" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_32711da5-cda7-44c0-8232-aa0381dbab32" xlink:to="loc_us-gaap_DepreciationDepletionAndAmortization_b34bc44f-9eea-44b1-8108-d7c7f6006ab3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_aa0b6747-90a3-4515-9ccd-63a74296413c" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_7b24fc3c-baf3-49a3-86ad-de9a4d15e387" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_aa0b6747-90a3-4515-9ccd-63a74296413c" xlink:to="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_7b24fc3c-baf3-49a3-86ad-de9a4d15e387" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_9315f019-f6a9-48bc-90b4-1f628cacbf2d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_aa0b6747-90a3-4515-9ccd-63a74296413c" xlink:to="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_9315f019-f6a9-48bc-90b4-1f628cacbf2d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_f2ef9fbe-f9f0-4c54-b1d5-4ca2b5ecae76" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_aa0b6747-90a3-4515-9ccd-63a74296413c" xlink:to="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_f2ef9fbe-f9f0-4c54-b1d5-4ca2b5ecae76" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/INVENTORIESDetails" xlink:type="simple" xlink:href="cmpo-20230930.xsd#INVENTORIESDetails"/>
  <link:calculationLink xlink:role="http://composecure.com/role/INVENTORIESDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet_180284b9-29d7-421d-a2f1-c0343823c07b" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryNet"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryValuationReserves_1b489142-3423-47ff-99ab-968a6a7fe6b2" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryValuationReserves"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_InventoryNet_180284b9-29d7-421d-a2f1-c0343823c07b" xlink:to="loc_us-gaap_InventoryValuationReserves_1b489142-3423-47ff-99ab-968a6a7fe6b2" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryFinishedGoods_07eeb1a8-7e4f-463a-aa7f-071d5ec0a833" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryFinishedGoods"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_InventoryNet_180284b9-29d7-421d-a2f1-c0343823c07b" xlink:to="loc_us-gaap_InventoryFinishedGoods_07eeb1a8-7e4f-463a-aa7f-071d5ec0a833" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryRawMaterials_869100bc-7c5f-4d77-82c6-e451fa2460dd" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryRawMaterials"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_InventoryNet_180284b9-29d7-421d-a2f1-c0343823c07b" xlink:to="loc_us-gaap_InventoryRawMaterials_869100bc-7c5f-4d77-82c6-e451fa2460dd" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryWorkInProcess_e748fc2a-9e94-4ccc-9d38-65542248a57c" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryWorkInProcess"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_InventoryNet_180284b9-29d7-421d-a2f1-c0343823c07b" xlink:to="loc_us-gaap_InventoryWorkInProcess_e748fc2a-9e94-4ccc-9d38-65542248a57c" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/PROPERTYANDEQUIPMENTComponentsDetails" xlink:type="simple" xlink:href="cmpo-20230930.xsd#PROPERTYANDEQUIPMENTComponentsDetails"/>
  <link:calculationLink xlink:role="http://composecure.com/role/PROPERTYANDEQUIPMENTComponentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet_9c4f9971-f9d1-4bc0-bdcd-836d428a95f5" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_583ed589-beaa-47f1-bf41-c9718d7230c9" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet_9c4f9971-f9d1-4bc0-bdcd-836d428a95f5" xlink:to="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_583ed589-beaa-47f1-bf41-c9718d7230c9" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentGross_b1195a1e-3de1-4ce7-b875-5bc9b6236103" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentGross"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet_9c4f9971-f9d1-4bc0-bdcd-836d428a95f5" xlink:to="loc_us-gaap_PropertyPlantAndEquipmentGross_b1195a1e-3de1-4ce7-b875-5bc9b6236103" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/DEBTMaturityDetails" xlink:type="simple" xlink:href="cmpo-20230930.xsd#DEBTMaturityDetails"/>
  <link:calculationLink xlink:role="http://composecure.com/role/DEBTMaturityDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount_e4c63b89-0ed3-4b68-841c-62b94e1b5b73" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_b3d97ff1-8be5-48d2-bc0c-3d80daaa70e5" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount_e4c63b89-0ed3-4b68-841c-62b94e1b5b73" xlink:to="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_b3d97ff1-8be5-48d2-bc0c-3d80daaa70e5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_968179dd-e3c1-4ddb-b3b1-9e9cf2db820e" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount_e4c63b89-0ed3-4b68-841c-62b94e1b5b73" xlink:to="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_968179dd-e3c1-4ddb-b3b1-9e9cf2db820e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_55ee5883-c068-41bb-b7ba-80de5076f348" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount_e4c63b89-0ed3-4b68-841c-62b94e1b5b73" xlink:to="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_55ee5883-c068-41bb-b7ba-80de5076f348" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_cd3a94ae-ef0f-444a-94cb-75ec59df9205" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount_e4c63b89-0ed3-4b68-841c-62b94e1b5b73" xlink:to="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_cd3a94ae-ef0f-444a-94cb-75ec59df9205" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/EARNINGSPERSHAREBasicandDilutedCalculationDetails" xlink:type="simple" xlink:href="cmpo-20230930.xsd#EARNINGSPERSHAREBasicandDilutedCalculationDetails"/>
  <link:calculationLink xlink:role="http://composecure.com/role/EARNINGSPERSHAREBasicandDilutedCalculationDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_942cdd9e-ff22-4d17-a9de-9ae07d43e0cb" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_b6233cbd-8d88-4978-9d95-e1b1a833b728" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_942cdd9e-ff22-4d17-a9de-9ae07d43e0cb" xlink:to="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_b6233cbd-8d88-4978-9d95-e1b1a833b728" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_65646435-9248-49a0-92f8-4efcdbd1220d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_942cdd9e-ff22-4d17-a9de-9ae07d43e0cb" xlink:to="loc_us-gaap_ProfitLoss_65646435-9248-49a0-92f8-4efcdbd1220d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_e8397340-327c-48dc-8c36-3ec4b1f145d8" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_b08385a2-6c61-40ec-a534-0989fe2a3901" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_e8397340-327c-48dc-8c36-3ec4b1f145d8" xlink:to="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_b08385a2-6c61-40ec-a534-0989fe2a3901" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DilutiveSecurities_bbd69025-7e41-42c3-8a18-ffc4417840e3" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DilutiveSecurities"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_e8397340-327c-48dc-8c36-3ec4b1f145d8" xlink:to="loc_us-gaap_DilutiveSecurities_bbd69025-7e41-42c3-8a18-ffc4417840e3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_f875045b-c6a4-4ff9-bb44-18653e6753d6" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_3ee16fbb-902a-4ed0-b7d0-c5361425e796" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_f875045b-c6a4-4ff9-bb44-18653e6753d6" xlink:to="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_3ee16fbb-902a-4ed0-b7d0-c5361425e796" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_03965db7-aa99-48ff-ad68-b7a17926dbdd" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_f875045b-c6a4-4ff9-bb44-18653e6753d6" xlink:to="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_03965db7-aa99-48ff-ad68-b7a17926dbdd" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/COMMITMENTSANDCONTINGENCIESLeasesDetails" xlink:type="simple" xlink:href="cmpo-20230930.xsd#COMMITMENTSANDCONTINGENCIESLeasesDetails"/>
  <link:calculationLink xlink:role="http://composecure.com/role/COMMITMENTSANDCONTINGENCIESLeasesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_0a022e90-e3a5-4cf2-b5c5-db2f418cbe4d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_8f191eca-a04d-44bf-b5b6-e12391afb96d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_0a022e90-e3a5-4cf2-b5c5-db2f418cbe4d" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_8f191eca-a04d-44bf-b5b6-e12391afb96d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_9b316207-a7a2-4e65-ae61-06ac4bbe005d" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_0a022e90-e3a5-4cf2-b5c5-db2f418cbe4d" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_9b316207-a7a2-4e65-ae61-06ac4bbe005d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_96ef6431-85a0-4e29-962f-3fa567eecdf5" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_0a022e90-e3a5-4cf2-b5c5-db2f418cbe4d" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_96ef6431-85a0-4e29-962f-3fa567eecdf5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_19151e8a-b1b4-4257-97d9-f0650b4f0c17" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_0a022e90-e3a5-4cf2-b5c5-db2f418cbe4d" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_19151e8a-b1b4-4257-97d9-f0650b4f0c17" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_e633db92-3420-493d-8a46-91ff35c0faef" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_0a022e90-e3a5-4cf2-b5c5-db2f418cbe4d" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_e633db92-3420-493d-8a46-91ff35c0faef" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_fd573e08-70eb-4ca0-8ef2-2927e2b797b0" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_0a022e90-e3a5-4cf2-b5c5-db2f418cbe4d" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_fd573e08-70eb-4ca0-8ef2-2927e2b797b0" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/COMMITMENTSANDCONTINGENCIESLeasesDetails_1" xlink:type="simple" xlink:href="cmpo-20230930.xsd#COMMITMENTSANDCONTINGENCIESLeasesDetails_1"/>
  <link:calculationLink xlink:role="http://composecure.com/role/COMMITMENTSANDCONTINGENCIESLeasesDetails_1" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_60a6a575-840c-4c63-9078-2f6c55e9e592" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability_682ccadf-0c1e-4e4c-9578-d21349d45db5" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_60a6a575-840c-4c63-9078-2f6c55e9e592" xlink:to="loc_us-gaap_OperatingLeaseLiability_682ccadf-0c1e-4e4c-9578-d21349d45db5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_85e49792-432c-4b2e-9fa7-f1e13372482a" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_60a6a575-840c-4c63-9078-2f6c55e9e592" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_85e49792-432c-4b2e-9fa7-f1e13372482a" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://composecure.com/role/COMMITMENTSANDCONTINGENCIESTaxReceivableAgreementDetails" xlink:type="simple" xlink:href="cmpo-20230930.xsd#COMMITMENTSANDCONTINGENCIESTaxReceivableAgreementDetails"/>
  <link:calculationLink xlink:role="http://composecure.com/role/COMMITMENTSANDCONTINGENCIESTaxReceivableAgreementDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiability_ebc05e35-ea71-4a3d-a3a2-753a7f9dc756" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiability"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearThree_ee30c4d0-52c7-45fe-a8ad-551e8d47058b" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityToBePaidYearThree"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_cmpo_TaxReceivableAgreementLiability_ebc05e35-ea71-4a3d-a3a2-753a7f9dc756" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearThree_ee30c4d0-52c7-45fe-a8ad-551e8d47058b" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearOne_b48823cb-1f4f-4168-9707-e82acad68e22" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityToBePaidYearOne"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_cmpo_TaxReceivableAgreementLiability_ebc05e35-ea71-4a3d-a3a2-753a7f9dc756" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearOne_b48823cb-1f4f-4168-9707-e82acad68e22" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearTwo_e41e103e-a44c-4b17-a109-1f65a8beffba" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityToBePaidYearTwo"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_cmpo_TaxReceivableAgreementLiability_ebc05e35-ea71-4a3d-a3a2-753a7f9dc756" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearTwo_e41e103e-a44c-4b17-a109-1f65a8beffba" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidAfterYearFour_c973fc9a-aac7-4395-9184-aded2e1ce45a" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityToBePaidAfterYearFour"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_cmpo_TaxReceivableAgreementLiability_ebc05e35-ea71-4a3d-a3a2-753a7f9dc756" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidAfterYearFour_c973fc9a-aac7-4395-9184-aded2e1ce45a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidRemainderOfFiscalYear_94f7450b-7f73-409f-80b4-3f172caca440" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityToBePaidRemainderOfFiscalYear"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_cmpo_TaxReceivableAgreementLiability_ebc05e35-ea71-4a3d-a3a2-753a7f9dc756" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidRemainderOfFiscalYear_94f7450b-7f73-409f-80b4-3f172caca440" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearFour_fd49295f-7bfa-43f6-8d64-0012a6f3f174" xlink:href="cmpo-20230930.xsd#cmpo_TaxReceivableAgreementLiabilityToBePaidYearFour"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="loc_cmpo_TaxReceivableAgreementLiability_ebc05e35-ea71-4a3d-a3a2-753a7f9dc756" xlink:to="loc_cmpo_TaxReceivableAgreementLiabilityToBePaidYearFour_fd49295f-7bfa-43f6-8d64-0012a6f3f174" xlink:type="arc"/>
  </link:calculationLink>
</link:linkbase>
