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SEC EDGAR · Insider purchase

COR: Tyler Lauren M 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
Jun 24, 2026, 4:04 PM EDT
Event / period date
Jun 22, 2026
Collected
Nov 9, 2026, 11:46 PM 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

Tyler Lauren M (Director)

550 shares · Common Stock

Jun 22, 2026 · $270.23 per share

Value calculated from the reported shares and prices: $148,626.50.

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>2026-06-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001765744</rptOwnerCik>
            <rptOwnerName>Tyler Lauren M</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>2026-06-22</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>550</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>270.23</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4359</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 Lauren M. Tyler</signatureName>
        <signatureDate>2026-06-24</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.