<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Linkbase Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2023-02-28T12:25:14.5295+00:00 -->
<!-- Copyright (c) 2023 Donnelly Financial Solutions, Inc. All Rights Reserved. -->
<link:linkbase xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" 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">
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_StatementConsolidatedBalanceSheets" xlink:href="fate-20221231.xsd#Role_StatementConsolidatedBalanceSheets" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/DisclosureIncomeTaxesDetails23" xlink:href="fate-20221231.xsd#DisclosureIncomeTaxesDetails23" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/DisclosureLeasesDetails22" xlink:href="fate-20221231.xsd#DisclosureLeasesDetails22" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_StatementConsolidatedStatementsOfOperationsAndComprehensiveLoss" xlink:href="fate-20221231.xsd#Role_StatementConsolidatedStatementsOfOperationsAndComprehensiveLoss" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_StatementConsolidatedStatementsOfCashFlows" xlink:href="fate-20221231.xsd#Role_StatementConsolidatedStatementsOfCashFlows" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureOrganizationAndSummaryOfSignificantAccountingPoliciesDetails1" xlink:href="fate-20221231.xsd#Role_DisclosureOrganizationAndSummaryOfSignificantAccountingPoliciesDetails1" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosurePropertyAndEquipmentDetails" xlink:href="fate-20221231.xsd#Role_DisclosurePropertyAndEquipmentDetails" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureAccruedExpensesAndLongTermDebtDetails" xlink:href="fate-20221231.xsd#Role_DisclosureAccruedExpensesAndLongTermDebtDetails" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureLeasesDetails1" xlink:href="fate-20221231.xsd#Role_DisclosureLeasesDetails1" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureLeasesDetails2" xlink:href="fate-20221231.xsd#Role_DisclosureLeasesDetails2" xlink:type="simple"/>
  <link:roleRef roleURI="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureIncomeTaxesDetails" xlink:href="fate-20221231.xsd#Role_DisclosureIncomeTaxesDetails" xlink:type="simple"/>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_StatementConsolidatedBalanceSheets">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesCurrent" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_AccountsPayableCurrent" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_AssetsCurrent" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_PreferredStockValue" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_ContractWithCustomerLiabilityNoncurrent" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_AccruedLiabilitiesCurrent" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_LongTermInvestments" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_CommonStockValue" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="fate_CIRMAwardLiabilityNoncurrent" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="fate_CIRMAwardLiabilityCurrent" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_ShortTermInvestments" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_PropertyPlantAndEquipmentNet" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_AdditionalPaidInCapital" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_ContractWithCustomerLiabilityCurrent" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="fate_StockPriceAppreciationMilestonesLiabilitiesNonCurrent" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_PrepaidExpenseAndOtherAssetsCurrent" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_RestrictedCashNoncurrent" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_CommitmentsAndContingencies" order="5" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_ContractWithCustomerAssetNetNoncurrent" order="5" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_StockholdersEquity" order="6" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OtherAssetsNoncurrent" order="6" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PreferredStockValue" xlink:label="us-gaap_PreferredStockValue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ContractWithCustomerLiabilityNoncurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccruedLiabilitiesCurrent" xlink:label="us-gaap_AccruedLiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccountsReceivableNetCurrent" xlink:label="us-gaap_AccountsReceivableNetCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LongTermInvestments" xlink:label="us-gaap_LongTermInvestments"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_CIRMAwardLiabilityNoncurrent" xlink:label="fate_CIRMAwardLiabilityNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_CIRMAwardLiabilityCurrent" xlink:label="fate_CIRMAwardLiabilityCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ShortTermInvestments" xlink:label="us-gaap_ShortTermInvestments"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ContractWithCustomerLiabilityCurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_StockPriceAppreciationMilestonesLiabilitiesNonCurrent" xlink:label="fate_StockPriceAppreciationMilestonesLiabilitiesNonCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingLeaseLiabilityCurrent" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RestrictedCashNoncurrent" xlink:label="us-gaap_RestrictedCashNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:label="us-gaap_ContractWithCustomerAssetNetNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherAssetsNoncurrent" xlink:label="us-gaap_OtherAssetsNoncurrent"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/DisclosureIncomeTaxesDetails23">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="us-gaap_DeferredTaxAssetsGross" order="0" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="us-gaap_DeferredTaxLiabilities" order="0" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="fate_DeferredTaxLiabilitiesDepreciation" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="us-gaap_DeferredIncomeTaxLiabilities" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="us-gaap_DeferredTaxAssetsValuationAllowance" order="1" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="fate_DeferredTaxLiabilitiesRightOfUseAssets" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsGoodwillAndIntangibleAssets" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsDeferredIncome" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost" order="5" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="fate_DeferredTaxAssetsLeaseLiabilities" order="6" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsOther" order="7" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxLiabilities" xlink:label="us-gaap_DeferredTaxLiabilities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsGross" xlink:label="us-gaap_DeferredTaxAssetsGross"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredIncomeTaxLiabilities" xlink:label="us-gaap_DeferredIncomeTaxLiabilities"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_DeferredTaxLiabilitiesDepreciation" xlink:label="fate_DeferredTaxLiabilitiesDepreciation"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsValuationAllowance" xlink:label="us-gaap_DeferredTaxAssetsValuationAllowance"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_DeferredTaxLiabilitiesRightOfUseAssets" xlink:label="fate_DeferredTaxLiabilitiesRightOfUseAssets"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch" xlink:label="us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsGoodwillAndIntangibleAssets" xlink:label="us-gaap_DeferredTaxAssetsGoodwillAndIntangibleAssets"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsDeferredIncome" xlink:label="us-gaap_DeferredTaxAssetsDeferredIncome"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_DeferredTaxAssetsLeaseLiabilities" xlink:label="fate_DeferredTaxAssetsLeaseLiabilities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DeferredTaxAssetsOther" xlink:label="us-gaap_DeferredTaxAssetsOther"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/DisclosureLeasesDetails22">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_OperatingLeaseLiability" order="1" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingLeaseLiability" xlink:label="us-gaap_OperatingLeaseLiability"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_StatementConsolidatedStatementsOfOperationsAndComprehensiveLoss">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_ResearchAndDevelopmentExpense" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_NetIncomeLoss" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="us-gaap_InvestmentIncomeInterest" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingExpenses" order="1" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_GeneralAndAdministrativeExpense" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_OtherNonoperatingIncomeExpense" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="us-gaap_InterestExpense" order="1" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="fate_IncreaseDecreaseInFairValueOfStockPriceAppreciationMilestones" order="2" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="us-gaap_OtherNonoperatingIncome" order="3" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingExpenses" xlink:label="us-gaap_OperatingExpenses"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ResearchAndDevelopmentExpense" xlink:label="us-gaap_ResearchAndDevelopmentExpense"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherNonoperatingIncomeExpense" xlink:label="us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InvestmentIncomeInterest" xlink:label="us-gaap_InvestmentIncomeInterest"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InterestExpense" xlink:label="us-gaap_InterestExpense"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_IncreaseDecreaseInFairValueOfStockPriceAppreciationMilestones" xlink:label="fate_IncreaseDecreaseInFairValueOfStockPriceAppreciationMilestones"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherNonoperatingIncome" xlink:label="us-gaap_OtherNonoperatingIncome"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_StatementConsolidatedStatementsOfCashFlows">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="fate_ProceedsFromIssuanceOfCommonStockInConnectionWithCollaborationAgreement" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_ProfitLoss" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" order="0" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="fate_ProceedsFromPublicOfferingOfCommonStockAndIssuanceOfPreFundedWarrants" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fate_IncreaseDecreaseInRightOfUseAssetsAndLeaseLiabilitiesNet" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquireInvestments" order="1" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="fate_ProceedsFromCIRMAward" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable" order="2" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromIssuanceOfWarrants" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInContractWithCustomerLiability" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromStockOptionsExercised" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AllocatedShareBasedCompensationExpense" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromIssuanceOfPrivatePlacement" order="5" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" order="5" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fate_IncreaseDecreaseInFairValueOfStockPriceAppreciationMilestones" order="6" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_CapitalizedContractCostAmortization" order="7" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" order="8" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DepreciationDepletionAndAmortization" order="9" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" order="10" weight="-1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_ProceedsFromIssuanceOfCommonStockInConnectionWithCollaborationAgreement" xlink:label="fate_ProceedsFromIssuanceOfCommonStockInConnectionWithCollaborationAgreement"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_ProceedsFromPublicOfferingOfCommonStockAndIssuanceOfPreFundedWarrants" xlink:label="fate_ProceedsFromPublicOfferingOfCommonStockAndIssuanceOfPreFundedWarrants"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_IncreaseDecreaseInRightOfUseAssetsAndLeaseLiabilitiesNet" xlink:label="fate_IncreaseDecreaseInRightOfUseAssetsAndLeaseLiabilitiesNet"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PaymentsToAcquireInvestments" xlink:label="us-gaap_PaymentsToAcquireInvestments"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_ProceedsFromCIRMAward" xlink:label="fate_ProceedsFromCIRMAward"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments" xlink:label="us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromIssuanceOfWarrants" xlink:label="us-gaap_ProceedsFromIssuanceOfWarrants"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromStockOptionsExercised" xlink:label="us-gaap_ProceedsFromStockOptionsExercised"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AllocatedShareBasedCompensationExpense" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_IncreaseDecreaseInFairValueOfStockPriceAppreciationMilestones" xlink:label="fate_IncreaseDecreaseInFairValueOfStockPriceAppreciationMilestones"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CapitalizedContractCostAmortization" xlink:label="us-gaap_CapitalizedContractCostAmortization"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DepreciationDepletionAndAmortization" xlink:label="us-gaap_DepreciationDepletionAndAmortization"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureOrganizationAndSummaryOfSignificantAccountingPoliciesDetails1">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:to="us-gaap_RestrictedCashAndCashEquivalentsNoncurrent" order="1" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RestrictedCashAndCashEquivalentsNoncurrent" xlink:label="us-gaap_RestrictedCashAndCashEquivalentsNoncurrent"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosurePropertyAndEquipmentDetails">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentGross" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" order="1" weight="-1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PropertyPlantAndEquipmentGross" xlink:label="us-gaap_PropertyPlantAndEquipmentGross"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureAccruedExpensesAndLongTermDebtDetails">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AccruedLiabilitiesCurrent" xlink:to="us-gaap_AccruedSalariesCurrent" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AccruedLiabilitiesCurrent" xlink:to="fate_AccruedClinicalTrialRelatedCostsCurrent" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AccruedLiabilitiesCurrent" xlink:to="us-gaap_OtherAccruedLiabilitiesCurrent" order="2" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccruedLiabilitiesCurrent" xlink:label="us-gaap_AccruedLiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccruedSalariesCurrent" xlink:label="us-gaap_AccruedSalariesCurrent"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_AccruedClinicalTrialRelatedCostsCurrent" xlink:label="fate_AccruedClinicalTrialRelatedCostsCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherAccruedLiabilitiesCurrent" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureLeasesDetails1">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingLeaseCost" xlink:to="us-gaap_StraightLineRentAdjustments" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingLeaseCost" xlink:to="us-gaap_VariableLeaseCost" order="1" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingLeaseCost" xlink:label="us-gaap_OperatingLeaseCost"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_StraightLineRentAdjustments" xlink:label="us-gaap_StraightLineRentAdjustments"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_VariableLeaseCost" xlink:label="us-gaap_VariableLeaseCost"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureLeasesDetails2">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" order="5" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://www.fatetherapeutics.com/20221231/taxonomy/role/Role_DisclosureIncomeTaxesDetails">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="fate_IncomeTaxReconciliationNondeductibleCompensation" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="fate_IncomeTaxReconciliationPermanentTaxDifferences" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationTaxCreditsResearch" order="5" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="fate_IncomeTaxReconciliationReserveForUncertainTaxPositions" order="6" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationOtherAdjustments" order="7" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" order="8" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_IncomeTaxReconciliationNondeductibleCompensation" xlink:label="fate_IncomeTaxReconciliationNondeductibleCompensation"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_IncomeTaxReconciliationPermanentTaxDifferences" xlink:label="fate_IncomeTaxReconciliationPermanentTaxDifferences"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxReconciliationTaxCreditsResearch" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsResearch"/>
    <link:loc xlink:type="locator" xlink:href="fate-20221231.xsd#fate_IncomeTaxReconciliationReserveForUncertainTaxPositions" xlink:label="fate_IncomeTaxReconciliationReserveForUncertainTaxPositions"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:label="us-gaap_IncomeTaxReconciliationOtherAdjustments"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:label="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
  </link:calculationLink>
</link:linkbase>
