<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2024-02-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000009984</issuerCik>
        <issuerName>BARNES GROUP INC</issuerName>
        <issuerTradingSymbol>B</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001175893</rptOwnerCik>
            <rptOwnerName>MANGUM MYLLE H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>BARNES GROUP INC.</rptOwnerStreet1>
            <rptOwnerStreet2>123 MAIN STREET</rptOwnerStreet2>
            <rptOwnerCity>BRISTOL</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06010</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2024-02-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1033</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27399.69</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Reporting Person has received 1,033 Restricted Stock Units that are subject to forfeiture if certain events occur and are payable in shares of common stock on or as soon as practicable following the applicable vesting date.</footnote>
        <footnote id="F2">Includes (a) a balance of 973 Restricted Stock Units granted 5/19/2023, which are subject to forfeiture if certain events occur and payable in shares of common stock on or as soon as practicable following the applicable vesting date, (b) 12,000 shares of deferred stock under the Non-Employee Director Deferred Stock Plan, which are payable in shares of common stock upon separation from service as a director, and (c) 13,393.69 shares of common stock, which includes 10.205236 shares from dividends reinvested on 12/08/2023.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Mylle H. Mangum by Daniela Rivera under Power of Attorney</signatureName>
        <signatureDate>2024-02-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
