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SEC EDGAR · Insider purchase

COR: DURCAN DERMOT MARK reported buying shares

1 reported purchase of non-derivative securities. Code P includes open-market and private purchases; it does not establish motive.

Follow COR
Became public
May 28, 2026, 4:23 PM EDT
Event / period date
May 28, 2026
Collected
Nov 10, 2026, 8:07 AM EST

Why this is connected

This filing identifies Cencora, Inc. as the issuer of the security. The company's SEC identifier connects it to COR.

Open the original source ↗Follow company activity in COR

Reported transactions

DURCAN DERMOT MARK (Director)

4,000 shares · Common Stock

May 28, 2026 · $266.26 per share

Value calculated from the reported shares and prices: $1,065,040.00.

Code P covers open-market and private purchases. Grants, option exercises, and tax withholding are excluded from purchase results. Read the source footnotes for ownership and pricing details.

Source evidence

Read the source excerpt or record
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-05-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001140859</issuerCik>
        <issuerName>Cencora, Inc.</issuerName>
        <issuerTradingSymbol>COR</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001202358</rptOwnerCik>
            <rptOwnerName>DURCAN DERMOT MARK</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>1 WEST FIRST AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CONSHOHOCKEN</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19428</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-05-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>266.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27767</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Elizabeth S. Campbell, attorney-in-fact for D. Mark Durcan</signatureName>
        <signatureDate>2026-05-28</signatureDate>
    </ownerSignature>
</ownershipDocument>

Congressional trading in COR

These disclosures provide context. Their presence does not establish a link between a trader and the event.

Original documents control. Public records can be amended, and company connections may require interpretation. Nothing here is investment advice.