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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-12-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000095953</issuerCik>
        <issuerName>SYNALLOY CORP</issuerName>
        <issuerTradingSymbol>SYNL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001520557</rptOwnerCik>
            <rptOwnerName>Rosenzweig Benjamin L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>79 WEST PACES FERRY ROAD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 200</rptOwnerStreet2>
            <rptOwnerCity>ATLANTA</rptOwnerCity>
            <rptOwnerState>GA</rptOwnerState>
            <rptOwnerZipCode>30305</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-12-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3517</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>41773</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Subscription Rights (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>12.75</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-12-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3517</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-11-30</value>
            </exerciseDate>
            <expirationDate>
                <value>2021-12-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3517.0</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>0</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On November 30, 2021, the issuer commenced a rights offering pursuant to which the issuer distributed non transferable subscription rights (the &quot;Subscription Rights&quot;) to holders of record of it common stock as of 5:00 p.m. New York Time, on November 29, 2021. Each eligible recordholder received on Subscription Right for each share of common stock held of record by such holder as of the record date. Each Subscription Right entitled its holder, subject to certain limitations and conditions, to purchase 0.083768 shares of common stock at a subscription price of $12.75 per whole share. Holders of Subscription Rights that exercised in full such basic subscription rights were entitled, subject to certain limitations and conditions, to oversubscribe for additional shares of common stock that remained unsubscribed for the rights offering. The rights offering expired on December 16, 2021 and the Company announced the results of the offering on December 17, 2021.</footnote>
        <footnote id="F2">Shares directly acquired by the reporting person as a result of their exercise of subscription rights and oversubscription privilege in connection with the issuer's rights offering.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Pauline A. Sumner, Power of Attorney for Benjamin Rosenzweig</signatureName>
        <signatureDate>2021-12-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2021-12-16
0
0000095953
SYNALLOY CORP
SYNL
0001520557
Rosenzweig Benjamin L
79 WEST PACES FERRY ROAD
SUITE 200
ATLANTA
GA
30305
1
0
0
0
Common Stock
2021-12-16
4
M
0
3517
12.75
A
41773
D
Subscription Rights (Right to Buy)
12.75
2021-12-16
4
M
0
3517
0
D
2021-11-30
2021-12-16
Common Stock
3517.0
0
D
On November 30, 2021, the issuer commenced a rights offering pursuant to which the issuer distributed non transferable subscription rights (the "Subscription Rights") to holders of record of it common stock as of 5:00 p.m. New York Time, on November 29, 2021. Each eligible recordholder received on Subscription Right for each share of common stock held of record by such holder as of the record date. Each Subscription Right entitled its holder, subject to certain limitations and conditions, to purchase 0.083768 shares of common stock at a subscription price of $12.75 per whole share. Holders of Subscription Rights that exercised in full such basic subscription rights were entitled, subject to certain limitations and conditions, to oversubscribe for additional shares of common stock that remained unsubscribed for the rights offering. The rights offering expired on December 16, 2021 and the Company announced the results of the offering on December 17, 2021.
Shares directly acquired by the reporting person as a result of their exercise of subscription rights and oversubscription privilege in connection with the issuer's rights offering.
Pauline A. Sumner, Power of Attorney for Benjamin Rosenzweig
2021-12-27