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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-08-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001201033</rptOwnerCik>
            <rptOwnerName>PARNELL LINDSEY KENNETH</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior Vice President</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-08-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>50000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.028</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>146270</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 $18.028. The shares were sold in multiple transactions at prices ranging from $18.00 to $18.18 per share, inclusive.  The reporting person will provide to Interface, Inc., any security holder of Interface, Inc., or the staff of the Securities and Exchange Commission, upon request, full informaton regarding the number of shares sold at each separate 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>2013-08-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
