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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-05-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000715787</issuerCik>
        <issuerName>INTERFACE INC</issuerName>
        <issuerTradingSymbol>TILE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001115331</rptOwnerCik>
            <rptOwnerName>KENNEDY CHRISTOPHER G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2859  PACES FERRY ROAD</rptOwnerStreet1>
            <rptOwnerStreet2>OVERLOOK III, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>ATLANTA</rptOwnerCity>
            <rptOwnerState>GA</rptOwnerState>
            <rptOwnerZipCode>30339</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>2015-05-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>18000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.9252</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>94273</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Reflects a weighted average sale price of $21.9252. The shares were sold in multiple transactions at prices ranging from $21.81 to $22.07 per share, inclusive. The reporting person will provide to Interface, Inc., such security holder of Interface, Inc., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each price within the range set forth herein.</footnote>
        <footnote id="F2">A substantial number of such shares are restricted shares subject to a risk of forfeiture under certain circumstances.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ David B. Foshee, Attorney in Fact</signatureName>
        <signatureDate>2015-05-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
