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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-09-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000070487</issuerCik>
        <issuerName>NATIONAL RESEARCH CORP</issuerName>
        <issuerTradingSymbol>NRC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001729470</rptOwnerCik>
            <rptOwnerName>Amandla MK Trust</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BRYN MAWR TRUST COMPANY OF DELAW</rptOwnerStreet1>
            <rptOwnerStreet2>20 MONTCHANIN RD, SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>GREENVILLE</rptOwnerCity>
            <rptOwnerState>DE</rptOwnerState>
            <rptOwnerZipCode>19807</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-09-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1063</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>64.8468</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7040473</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Amandla II, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price in Column 4 is a weighted average price. The prices actually received ranged from $64.75 to $64.99. The reporting person has provided to the issuer, and will provide to any security holder of the issuer, or the SEC staff, upon request, information regarding the number of shares sold at each price within the range for all transactions reported in this Form 4 utilizing an average weighted price.</footnote>
    </footnotes>

    <remarks>This Form 4 is being filed by the Amandla MK Trust and by Patrick E. Beans, as Special Holdings Direction Adviser under the Amandla MK Trust.</remarks>

    <ownerSignature>
        <signatureName>/s/ Russell E. Ryba, Attorney-in-Fact for Patrick E. Beans, as Special Holdings Direction Adviser</signatureName>
        <signatureDate>2019-09-05</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Russell E. Ryba, Attorney-in-Fact for Patrick E. Beans, as Special Holdings Direction Adviser under the Amandla MK Trust</signatureName>
        <signatureDate>2019-09-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
