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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019e9408-0626-72eb-aae0-d2e2b0b7ff42,g:0a086f49-9852-41bd-8794-bdf62807007f-->
<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:arcroleRef arcroleURI="https://xbrl.org/2023/arcrole/summation-item" xlink:type="simple" xlink:href="https://www.xbrl.org/2023/calculation-1.1.xsd#summation-item"/>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/CONDENSEDCONSOLIDATEDBALANCESHEETS" xlink:type="simple" xlink:href="brns-20260630.xsd#CONDENSEDCONSOLIDATEDBALANCESHEETS"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/CONDENSEDCONSOLIDATEDBALANCESHEETS" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent_019e9408-06cc-737f-be79-713dcfb2509c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent_019e9408-06cc-7f11-af8c-46a0d5d6f374" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e9408-06cc-737f-be79-713dcfb2509c" xlink:to="loc_us-gaap_AccountsPayableCurrent_019e9408-06cc-7f11-af8c-46a0d5d6f374" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7f16-bb0d-0f8492fd8b6f" xlink:href="brns-20260630.xsd#brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e9408-06cc-737f-be79-713dcfb2509c" xlink:to="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7f16-bb0d-0f8492fd8b6f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeCurrent_019e9408-06cc-7fb6-ab37-b006df992449" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeCurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e9408-06cc-737f-be79-713dcfb2509c" xlink:to="loc_us-gaap_DeferredIncomeCurrent_019e9408-06cc-7fb6-ab37-b006df992449" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent_019e9408-06cc-7c8c-836d-d2ee34b3d1ad" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e9408-06cc-737f-be79-713dcfb2509c" xlink:to="loc_us-gaap_OperatingLeaseLiabilityCurrent_019e9408-06cc-7c8c-836d-d2ee34b3d1ad" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e9408-06cc-75aa-b8c5-e9b2cf670a6e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_019e9408-06cc-7383-9d04-4dc6ba496beb" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e9408-06cc-75aa-b8c5-e9b2cf670a6e" xlink:to="loc_us-gaap_Liabilities_019e9408-06cc-7383-9d04-4dc6ba496beb" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies_019e9408-06cc-7385-96f9-0f7d8d76dd66" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e9408-06cc-75aa-b8c5-e9b2cf670a6e" xlink:to="loc_us-gaap_CommitmentsAndContingencies_019e9408-06cc-7385-96f9-0f7d8d76dd66" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-7615-93b6-f3b9d0da9826" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e9408-06cc-75aa-b8c5-e9b2cf670a6e" xlink:to="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-7615-93b6-f3b9d0da9826" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_019e9408-06cc-7ceb-a7f2-6019cccd45dd" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e9408-06cc-719f-b2ef-3f2ab7ddc22e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e9408-06cc-7ceb-a7f2-6019cccd45dd" xlink:to="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e9408-06cc-719f-b2ef-3f2ab7ddc22e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashCurrent_019e9408-06cc-7c83-b3bf-bca38a2a7896" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e9408-06cc-7ceb-a7f2-6019cccd45dd" xlink:to="loc_us-gaap_RestrictedCashCurrent_019e9408-06cc-7c83-b3bf-bca38a2a7896" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_ResearchAndDevelopmentIncentivesReceivable_019e9408-06cc-7317-adf7-a07c65e4a076" xlink:href="brns-20260630.xsd#brns_ResearchAndDevelopmentIncentivesReceivable"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e9408-06cc-7ceb-a7f2-6019cccd45dd" xlink:to="loc_brns_ResearchAndDevelopmentIncentivesReceivable_019e9408-06cc-7317-adf7-a07c65e4a076" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e9408-06cc-7355-9675-4217928f7cb4" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e9408-06cc-7ceb-a7f2-6019cccd45dd" xlink:to="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e9408-06cc-7355-9675-4217928f7cb4" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_019e9408-06cc-7e15-baa8-0a1de9cf3250" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue_019e9408-06cc-77f0-bdc8-f59e0cc8325f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e9408-06cc-7e15-baa8-0a1de9cf3250" xlink:to="loc_us-gaap_CommonStockValue_019e9408-06cc-77f0-bdc8-f59e0cc8325f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_DeferredStockValueIssued_019e9408-06cc-7d1f-b2ac-ab632bc43f6d" xlink:href="brns-20260630.xsd#brns_DeferredStockValueIssued"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e9408-06cc-7e15-baa8-0a1de9cf3250" xlink:to="loc_brns_DeferredStockValueIssued_019e9408-06cc-7d1f-b2ac-ab632bc43f6d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital_019e9408-06cc-7ee4-9061-7f7637f67f0e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e9408-06cc-7e15-baa8-0a1de9cf3250" xlink:to="loc_us-gaap_AdditionalPaidInCapital_019e9408-06cc-7ee4-9061-7f7637f67f0e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit_019e9408-06cc-70b9-8861-1f458599a38f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e9408-06cc-7e15-baa8-0a1de9cf3250" xlink:to="loc_us-gaap_RetainedEarningsAccumulatedDeficit_019e9408-06cc-70b9-8861-1f458599a38f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax_019e9408-06cc-751a-8614-51462b40ea73" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e9408-06cc-7e15-baa8-0a1de9cf3250" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax_019e9408-06cc-751a-8614-51462b40ea73" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_019e9408-06cc-7da7-ab80-bc3c0cb77532" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent_019e9408-06cc-7d64-bc80-7b3ee9989350" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e9408-06cc-7da7-ab80-bc3c0cb77532" xlink:to="loc_us-gaap_LiabilitiesCurrent_019e9408-06cc-7d64-bc80-7b3ee9989350" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_019e9408-06cc-76f4-bf6d-1a8cb06c296f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e9408-06cc-7da7-ab80-bc3c0cb77532" xlink:to="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_019e9408-06cc-76f4-bf6d-1a8cb06c296f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_019e9408-06cc-7fb7-80a5-83a4b5b5aee2" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e9408-06cc-7da7-ab80-bc3c0cb77532" xlink:to="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_019e9408-06cc-7fb7-80a5-83a4b5b5aee2" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent_019e9408-06cc-7e7e-9d82-9127f8e7e5fd" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e9408-06cc-7da7-ab80-bc3c0cb77532" xlink:to="loc_us-gaap_OtherLiabilitiesNoncurrent_019e9408-06cc-7e7e-9d82-9127f8e7e5fd" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet_019e9408-06cc-7dde-9c73-4ddad8e2ba05" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e9408-06cc-7da7-ab80-bc3c0cb77532" xlink:to="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet_019e9408-06cc-7dde-9c73-4ddad8e2ba05" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-70bd-a3de-db3000640378" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest_019e9408-06cc-7c9e-988a-b4f48aa01669" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterest"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-70bd-a3de-db3000640378" xlink:to="loc_us-gaap_MinorityInterest_019e9408-06cc-7c9e-988a-b4f48aa01669" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_019e9408-06cc-7b05-a10e-7afe592a71db" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-70bd-a3de-db3000640378" xlink:to="loc_us-gaap_StockholdersEquity_019e9408-06cc-7b05-a10e-7afe592a71db" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets_019e9408-06cc-70a9-b9e3-a331a7e8cb2d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_019e9408-06cc-7b20-9d18-71156504b0c5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e9408-06cc-70a9-b9e3-a331a7e8cb2d" xlink:to="loc_us-gaap_AssetsCurrent_019e9408-06cc-7b20-9d18-71156504b0c5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet_019e9408-06cc-73ab-a7eb-907577fded99" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e9408-06cc-70a9-b9e3-a331a7e8cb2d" xlink:to="loc_us-gaap_PropertyPlantAndEquipmentNet_019e9408-06cc-73ab-a7eb-907577fded99" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill_019e9408-06cc-72d6-8149-705f1a932467" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e9408-06cc-70a9-b9e3-a331a7e8cb2d" xlink:to="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill_019e9408-06cc-72d6-8149-705f1a932467" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset_019e9408-06cc-7222-bab7-500d1df9a32a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e9408-06cc-70a9-b9e3-a331a7e8cb2d" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAsset_019e9408-06cc-7222-bab7-500d1df9a32a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets_019e9408-06cc-751f-99be-c64fde093c6b" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssets"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e9408-06cc-70a9-b9e3-a331a7e8cb2d" xlink:to="loc_us-gaap_OtherAssets_019e9408-06cc-751f-99be-c64fde093c6b" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/CONDENSEDCONSOLIDATEDSTATEMENTSOFOPERATIONSANDCOMPREHENSIVELOSS" xlink:type="simple" xlink:href="brns-20260630.xsd#CONDENSEDCONSOLIDATEDSTATEMENTSOFOPERATIONSANDCOMPREHENSIVELOSS"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/CONDENSEDCONSOLIDATEDSTATEMENTSOFOPERATIONSANDCOMPREHENSIVELOSS" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-71ff-ba3e-81d5061dae98" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e9408-06cc-7766-8e03-bd2bdfc6a9bf" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-71ff-ba3e-81d5061dae98" xlink:to="loc_us-gaap_ProfitLoss_019e9408-06cc-7766-8e03-bd2bdfc6a9bf" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_019e9408-06cc-709f-bc1a-27c4c5c3159a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-71ff-ba3e-81d5061dae98" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_019e9408-06cc-709f-bc1a-27c4c5c3159a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e9408-06cc-744c-9e51-52e7ca6dfefd" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss_019e9408-06cc-7742-9536-29e0965027e5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e9408-06cc-744c-9e51-52e7ca6dfefd" xlink:to="loc_us-gaap_OperatingIncomeLoss_019e9408-06cc-7742-9536-29e0965027e5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense_019e9408-06cc-7ac3-9879-dfc43985dc10" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e9408-06cc-744c-9e51-52e7ca6dfefd" xlink:to="loc_us-gaap_NonoperatingIncomeExpense_019e9408-06cc-7ac3-9879-dfc43985dc10" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss_019e9408-06cc-7509-b023-51b8c977ea17" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses_019e9408-06cc-7e35-9206-603828ed7afb" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingIncomeLoss_019e9408-06cc-7509-b023-51b8c977ea17" xlink:to="loc_us-gaap_OperatingExpenses_019e9408-06cc-7e35-9206-603828ed7afb" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingIncome_019e9408-06cc-7c27-9ae3-dd6aed0a2bd8" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherOperatingIncome"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingIncomeLoss_019e9408-06cc-7509-b023-51b8c977ea17" xlink:to="loc_us-gaap_OtherOperatingIncome_019e9408-06cc-7c27-9ae3-dd6aed0a2bd8" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses_019e9408-06cc-737e-8b3f-8ebcd5a0f2b9" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpense_019e9408-06cc-7648-9c26-7408e532cc5e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ResearchAndDevelopmentExpense"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingExpenses_019e9408-06cc-737e-8b3f-8ebcd5a0f2b9" xlink:to="loc_us-gaap_ResearchAndDevelopmentExpense_019e9408-06cc-7648-9c26-7408e532cc5e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense_019e9408-06cc-70bb-a39b-1d0ddab1476a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingExpenses_019e9408-06cc-737e-8b3f-8ebcd5a0f2b9" xlink:to="loc_us-gaap_GeneralAndAdministrativeExpense_019e9408-06cc-70bb-a39b-1d0ddab1476a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019f5d4d-4054-7616-80de-971630d209ae" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019f5d4d-4054-765b-a419-ead28d346782" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019f5d4d-4054-7616-80de-971630d209ae" xlink:to="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019f5d4d-4054-765b-a419-ead28d346782" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense_019e9408-06cc-7333-93eb-33990be925a5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest_019e9408-06cc-7167-9590-cfa3e8c5cfb7" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_019e9408-06cc-7333-93eb-33990be925a5" xlink:to="loc_us-gaap_InvestmentIncomeInterest_019e9408-06cc-7167-9590-cfa3e8c5cfb7" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating_019e9408-06cc-7abd-b874-c657438e04f0" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_019e9408-06cc-7333-93eb-33990be925a5" xlink:to="loc_us-gaap_InterestExpenseNonoperating_019e9408-06cc-7abd-b874-c657438e04f0" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_ResearchAndDevelopmentIncentiveIncomeExpense_019e9408-06cc-7049-b65d-a3c4ef1bb262" xlink:href="brns-20260630.xsd#brns_ResearchAndDevelopmentIncentiveIncomeExpense"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_019e9408-06cc-7333-93eb-33990be925a5" xlink:to="loc_brns_ResearchAndDevelopmentIncentiveIncomeExpense_019e9408-06cc-7049-b65d-a3c4ef1bb262" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense_019e9408-06cc-7221-8773-175fd651dd17" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NonoperatingIncomeExpense_019e9408-06cc-7333-93eb-33990be925a5" xlink:to="loc_us-gaap_OtherNonoperatingIncomeExpense_019e9408-06cc-7221-8773-175fd651dd17" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax_019e9408-06cc-7b11-b518-e9d73daa81b1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-7d6a-bd4d-07e5f13926a8" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax_019e9408-06cc-7b11-b518-e9d73daa81b1" xlink:to="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e9408-06cc-7d6a-bd4d-07e5f13926a8" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_019e9408-06cc-768b-b5d9-f315709fe596" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax_019e9408-06cc-7b11-b518-e9d73daa81b1" xlink:to="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_019e9408-06cc-768b-b5d9-f315709fe596" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e9408-06cc-7bcb-85c2-a498e735395a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e9408-06cc-7fe1-ab0f-6cd0770d7fef" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ProfitLoss_019e9408-06cc-7bcb-85c2-a498e735395a" xlink:to="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e9408-06cc-7fe1-ab0f-6cd0770d7fef" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit_019e9408-06cc-7ebe-8f95-486bc1645266" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ProfitLoss_019e9408-06cc-7bcb-85c2-a498e735395a" xlink:to="loc_us-gaap_IncomeTaxExpenseBenefit_019e9408-06cc-7ebe-8f95-486bc1645266" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss_019e9408-06cc-77c1-8b01-62ed46d5e741" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e9408-06cc-7bf0-a4fe-09ab75076b7e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLoss_019e9408-06cc-77c1-8b01-62ed46d5e741" xlink:to="loc_us-gaap_ProfitLoss_019e9408-06cc-7bf0-a4fe-09ab75076b7e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019e9408-06cc-7d1d-ba49-a0054721cae7" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLoss_019e9408-06cc-77c1-8b01-62ed46d5e741" xlink:to="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019e9408-06cc-7d1d-ba49-a0054721cae7" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/CONDENSEDCONSOLIDATEDSTATEMENTSOFCASHFLOWS" xlink:type="simple" xlink:href="brns-20260630.xsd#CONDENSEDCONSOLIDATEDSTATEMENTSOFCASHFLOWS"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/CONDENSEDCONSOLIDATEDSTATEMENTSOFCASHFLOWS" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e9408-06cc-7345-bb17-076cdbf9d3f5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_019e9408-06cc-7cb3-911e-10597714a086" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e9408-06cc-7345-bb17-076cdbf9d3f5" xlink:to="loc_us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_019e9408-06cc-7cb3-911e-10597714a086" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e9408-06cc-723d-9e70-b7ef8a785a81" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_019e9408-06cc-7228-b5ad-da8e92572aef" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e9408-06cc-723d-9e70-b7ef8a785a81" xlink:to="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_019e9408-06cc-7228-b5ad-da8e92572aef" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019e9408-06cc-7301-a435-7a98d3beba9a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e9408-06cc-723d-9e70-b7ef8a785a81" xlink:to="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019e9408-06cc-7301-a435-7a98d3beba9a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e9408-06cc-70be-9ca1-0c1af572631f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7ac6-a4a6-83b11324fc16" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e9408-06cc-70be-9ca1-0c1af572631f" xlink:to="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7ac6-a4a6-83b11324fc16" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e9408-06cc-7484-9c60-3a45f6a71608" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e9408-06cc-70be-9ca1-0c1af572631f" xlink:to="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e9408-06cc-7484-9c60-3a45f6a71608" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e9408-06cc-762c-a39c-4ac3bd7655d2" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e9408-06cc-70be-9ca1-0c1af572631f" xlink:to="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e9408-06cc-762c-a39c-4ac3bd7655d2" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019e9408-06cc-792c-8f15-a43e1a252bcc" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e9408-06cc-70be-9ca1-0c1af572631f" xlink:to="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019e9408-06cc-792c-8f15-a43e1a252bcc" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e9408-06cc-7bc7-939f-33f008452a04" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_ProfitLoss_019e9408-06cc-7bc7-939f-33f008452a04" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation_019e9408-06cc-7aa3-b542-64a74354d8ce" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_ShareBasedCompensation_019e9408-06cc-7aa3-b542-64a74354d8ce" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization_019e9408-06cc-75ed-8ff9-ccb700aaaa1f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_DepreciationDepletionAndAmortization_019e9408-06cc-75ed-8ff9-ccb700aaaa1f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_NonCashLeaseExpenses_019e9408-06cc-7e14-9289-69eec275ce1e" xlink:href="brns-20260630.xsd#brns_NonCashLeaseExpenses"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_brns_NonCashLeaseExpenses_019e9408-06cc-7e14-9289-69eec275ce1e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossUnrealized_019e9408-06cc-70cb-bf77-d662816ae0e2" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossUnrealized"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_ForeignCurrencyTransactionGainLossUnrealized_019e9408-06cc-70cb-bf77-d662816ae0e2" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_019e9408-06cc-7ed2-80f2-024337f06b10" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_019e9408-06cc-7ed2-80f2-024337f06b10" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_NonCashInterestExpenseOnConvertibleLoanNotes_019e9408-06cc-78fc-a20b-07e8f9917cf2" xlink:href="brns-20260630.xsd#brns_NonCashInterestExpenseOnConvertibleLoanNotes"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_brns_NonCashInterestExpenseOnConvertibleLoanNotes_019e9408-06cc-78fc-a20b-07e8f9917cf2" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit_019e9408-06cc-75c0-8f10-77bb912d25b2" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_DeferredIncomeTaxExpenseBenefit_019e9408-06cc-75c0-8f10-77bb912d25b2" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_019e9408-06cc-74da-8282-1808ed39f778" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment"/>
    <link:calculationArc order="9" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_019e9408-06cc-74da-8282-1808ed39f778" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_019e9408-06cc-70ed-938c-3fe94a568664" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:calculationArc order="10" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_019e9408-06cc-70ed-938c-3fe94a568664" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_IncreaseDecreaseInResearchAndDevelopmentIncentivesReceivable_019e9408-06cc-7594-bea9-4c4c61384f48" xlink:href="brns-20260630.xsd#brns_IncreaseDecreaseInResearchAndDevelopmentIncentivesReceivable"/>
    <link:calculationArc order="11" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_brns_IncreaseDecreaseInResearchAndDevelopmentIncentivesReceivable_019e9408-06cc-7594-bea9-4c4c61384f48" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayable_019e9408-06cc-7bca-90aa-9ed31e25397d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <link:calculationArc order="12" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_IncreaseDecreaseInAccountsPayable_019e9408-06cc-7bca-90aa-9ed31e25397d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019e9408-06cc-73e6-8118-a119fccdb39b" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities"/>
    <link:calculationArc order="13" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019e9408-06cc-73e6-8118-a119fccdb39b" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDeferredRevenue_019e9408-06cc-7efc-8313-9c91134c3370" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDeferredRevenue"/>
    <link:calculationArc order="14" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_IncreaseDecreaseInDeferredRevenue_019e9408-06cc-7efc-8313-9c91134c3370" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_019e9408-06cc-70f6-a550-354a9b05a863" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <link:calculationArc order="15" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e9408-06cc-7bef-8beb-c5ef20222765" xlink:to="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_019e9408-06cc-70f6-a550-354a9b05a863" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/SegmentinformationSignificantSegmentExpensesDetails" xlink:type="simple" xlink:href="brns-20260630.xsd#SegmentinformationSignificantSegmentExpensesDetails"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/SegmentinformationSignificantSegmentExpensesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpense_019e9408-06cc-7b29-bc55-2c2ce08ab92d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ResearchAndDevelopmentExpense"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_DirectResearchAndDevelopmentExpense_019e9408-06cc-7509-94d3-44ca919391bc" xlink:href="brns-20260630.xsd#brns_DirectResearchAndDevelopmentExpense"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpense_019e9408-06cc-7b29-bc55-2c2ce08ab92d" xlink:to="loc_brns_DirectResearchAndDevelopmentExpense_019e9408-06cc-7509-94d3-44ca919391bc" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_IndirectResearchAndDevelopmentExpense_019e9408-06cc-7f56-ad3b-b3f5ece2be16" xlink:href="brns-20260630.xsd#brns_IndirectResearchAndDevelopmentExpense"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpense_019e9408-06cc-7b29-bc55-2c2ce08ab92d" xlink:to="loc_brns_IndirectResearchAndDevelopmentExpense_019e9408-06cc-7f56-ad3b-b3f5ece2be16" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_ChangeInResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod_019e9408-06cc-7398-a03a-4eaa45af1f9f" xlink:href="brns-20260630.xsd#brns_ChangeInResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_ChangeInDirectResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod_019e9408-06cc-7f1a-ae70-fce0973abdf0" xlink:href="brns-20260630.xsd#brns_ChangeInDirectResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_ChangeInResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod_019e9408-06cc-7398-a03a-4eaa45af1f9f" xlink:to="loc_brns_ChangeInDirectResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod_019e9408-06cc-7f1a-ae70-fce0973abdf0" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_ChangeInIndirectResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod_019e9408-06cc-7595-b559-f5d19c8d71ef" xlink:href="brns-20260630.xsd#brns_ChangeInIndirectResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_ChangeInResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod_019e9408-06cc-7398-a03a-4eaa45af1f9f" xlink:to="loc_brns_ChangeInIndirectResearchAndDevelopmentExpenseCurrentPeriodComparedToPriorPeriod_019e9408-06cc-7595-b559-f5d19c8d71ef" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/PrepaidExpensesandOtherCurrentAssetsDetails" xlink:type="simple" xlink:href="brns-20260630.xsd#PrepaidExpensesandOtherCurrentAssetsDetails"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/PrepaidExpensesandOtherCurrentAssetsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e9408-06cc-713b-8327-e47f19872c8c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseCurrent_019e9408-06cc-7373-be1c-911df8135e94" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e9408-06cc-713b-8327-e47f19872c8c" xlink:to="loc_us-gaap_PrepaidExpenseCurrent_019e9408-06cc-7373-be1c-911df8135e94" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValueAddedTaxReceivableCurrent_019e9408-06cc-76d0-821c-5c7b5436ba37" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValueAddedTaxReceivableCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e9408-06cc-713b-8327-e47f19872c8c" xlink:to="loc_us-gaap_ValueAddedTaxReceivableCurrent_019e9408-06cc-76d0-821c-5c7b5436ba37" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsCurrent_019e9408-06cc-7711-ace0-8eb072a7162c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsCurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e9408-06cc-713b-8327-e47f19872c8c" xlink:to="loc_us-gaap_OtherAssetsCurrent_019e9408-06cc-7711-ace0-8eb072a7162c" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/AccruedExpensesandOtherCurrentLiabilitiesDetails" xlink:type="simple" xlink:href="brns-20260630.xsd#AccruedExpensesandOtherCurrentLiabilitiesDetails"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/AccruedExpensesandOtherCurrentLiabilitiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7640-a6b7-03f396f5d18b" xlink:href="brns-20260630.xsd#brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_AccruedManufacturingAndClinicalExpensesCurrent_019e9408-06cc-7eb8-b183-fab39799d202" xlink:href="brns-20260630.xsd#brns_AccruedManufacturingAndClinicalExpensesCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7640-a6b7-03f396f5d18b" xlink:to="loc_brns_AccruedManufacturingAndClinicalExpensesCurrent_019e9408-06cc-7eb8-b183-fab39799d202" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedBonusesCurrent_019e9408-06cc-7a19-8637-bd7d07e72851" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedBonusesCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7640-a6b7-03f396f5d18b" xlink:to="loc_us-gaap_AccruedBonusesCurrent_019e9408-06cc-7a19-8637-bd7d07e72851" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedEmployeeBenefitsCurrent_019e9408-06cc-7e9b-8434-58980d837457" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedEmployeeBenefitsCurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7640-a6b7-03f396f5d18b" xlink:to="loc_us-gaap_AccruedEmployeeBenefitsCurrent_019e9408-06cc-7e9b-8434-58980d837457" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedProfessionalFeesCurrent_019e9408-06cc-7146-9c4f-fa3adced11a8" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedProfessionalFeesCurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7640-a6b7-03f396f5d18b" xlink:to="loc_us-gaap_AccruedProfessionalFeesCurrent_019e9408-06cc-7146-9c4f-fa3adced11a8" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_AccruedGrantRepaymentCurrent_019e9408-06cc-7928-9044-850fc5664b7e" xlink:href="brns-20260630.xsd#brns_AccruedGrantRepaymentCurrent"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7640-a6b7-03f396f5d18b" xlink:to="loc_brns_AccruedGrantRepaymentCurrent_019e9408-06cc-7928-9044-850fc5664b7e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent_019e9408-06cc-72be-a89d-049d06830e68" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_brns_AccruedLiabilitiesAndOtherLiabilitiesCurrent_019e9408-06cc-7640-a6b7-03f396f5d18b" xlink:to="loc_us-gaap_OtherAccruedLiabilitiesCurrent_019e9408-06cc-72be-a89d-049d06830e68" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/ShareBasedCompensationScheduleofRestrictedStockUnitsActivityDetails" xlink:type="simple" xlink:href="brns-20260630.xsd#ShareBasedCompensationScheduleofRestrictedStockUnitsActivityDetails"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/ShareBasedCompensationScheduleofRestrictedStockUnitsActivityDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber_019e9408-06cc-73f3-bb31-d881176b337d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019e9408-06cc-72c2-a874-ce68adf6b659" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber_019e9408-06cc-73f3-bb31-d881176b337d" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019e9408-06cc-72c2-a874-ce68adf6b659" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedNumber_019e9408-06cc-78e1-aa57-edf50bde253d" xlink:href="brns-20260630.xsd#brns_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedNumber"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber_019e9408-06cc-73f3-bb31-d881176b337d" xlink:to="loc_brns_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedNumber_019e9408-06cc-78e1-aa57-edf50bde253d" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/CommitmentsandContingenciesLeaseCostDetails" xlink:type="simple" xlink:href="brns-20260630.xsd#CommitmentsandContingenciesLeaseCostDetails"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/CommitmentsandContingenciesLeaseCostDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost_019e9408-06cc-77d8-9947-522f19ae6804" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCost"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost_019e9408-06cc-7fdb-a5c1-6fcf6dccbb69" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseCost"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LeaseCost_019e9408-06cc-77d8-9947-522f19ae6804" xlink:to="loc_us-gaap_OperatingLeaseCost_019e9408-06cc-7fdb-a5c1-6fcf6dccbb69" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/CommitmentsandContingenciesMaturitiesofMinimumLeaseLiabilitiesDetails" xlink:type="simple" xlink:href="brns-20260630.xsd#CommitmentsandContingenciesMaturitiesofMinimumLeaseLiabilitiesDetails"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/CommitmentsandContingenciesMaturitiesofMinimumLeaseLiabilitiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-762b-ab9b-3da364de27f1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_019e9408-06cc-7034-a5bf-a969b93897a1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-762b-ab9b-3da364de27f1" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_019e9408-06cc-7034-a5bf-a969b93897a1" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019e9408-06cc-7b31-8641-5ac9e96714c8" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-762b-ab9b-3da364de27f1" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019e9408-06cc-7b31-8641-5ac9e96714c8" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019e9408-06cc-721e-a596-c8a5be8e5db7" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-762b-ab9b-3da364de27f1" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019e9408-06cc-721e-a596-c8a5be8e5db7" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019e9408-06cc-79d0-9ac2-e2ba3c1bc6db" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-762b-ab9b-3da364de27f1" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019e9408-06cc-79d0-9ac2-e2ba3c1bc6db" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019e9408-06cc-75db-af05-d98af9b74af5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-762b-ab9b-3da364de27f1" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019e9408-06cc-75db-af05-d98af9b74af5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_brns_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_019e9408-06cc-73e7-be74-759fa2e3d276" xlink:href="brns-20260630.xsd#brns_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-762b-ab9b-3da364de27f1" xlink:to="loc_brns_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_019e9408-06cc-73e7-be74-759fa2e3d276" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.barinthusbio.com/role/CommitmentsandContingenciesMaturitiesofMinimumLeaseLiabilitiesDetails_1" xlink:type="simple" xlink:href="brns-20260630.xsd#CommitmentsandContingenciesMaturitiesofMinimumLeaseLiabilitiesDetails_1"/>
  <link:calculationLink xlink:role="http://www.barinthusbio.com/role/CommitmentsandContingenciesMaturitiesofMinimumLeaseLiabilitiesDetails_1" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-7297-b7e4-31dac6f69978" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability_019e9408-06cc-74fb-9537-8c304ea2641a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-7297-b7e4-31dac6f69978" xlink:to="loc_us-gaap_OperatingLeaseLiability_019e9408-06cc-74fb-9537-8c304ea2641a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_019e9408-06cc-7d38-82c4-20c06ac0ef7e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e9408-06cc-7297-b7e4-31dac6f69978" xlink:to="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_019e9408-06cc-7d38-82c4-20c06ac0ef7e" xlink:type="arc"/>
  </link:calculationLink>
</link:linkbase>
