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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001579448</rptOwnerCik>
            <rptOwnerName>K/I/E Trust Under Agreement 10/24/18</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>BESSEMER TRUST COMPANY OF DELAWARE, N.A.</rptOwnerStreet1>
            <rptOwnerStreet2>1007 N. ORANGE ST., SUITE 1450</rptOwnerStreet2>
            <rptOwnerCity>WILMINGTON</rptOwnerCity>
            <rptOwnerState>DE</rptOwnerState>
            <rptOwnerZipCode>19801</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>2019-05-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>185088</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>40.0008</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4755013</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The reported transaction was effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person on May 21, 2018.</footnote>
        <footnote id="F2">The price in Column 4 is a weighted average price. The prices actually received ranged from $40.00 to $40.13. 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 K/I/E Trust Under Agreement 10/24/18, f/k/a the K/I/E/Trust Under Agreement 3/9/09, and by Patrick E. Beans, as Special Holdings Direction Adviser under The K/I/E Trust Under Agreement 10/24/18.</remarks>

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

    <ownerSignature>
        <signatureName>/s/ Russell E. Ryba, Attorney-in-Fact for Patrick E. Beans, Special Holdings Direction Adviser under the K/I/E Trust Under Agreement 10/24/18</signatureName>
        <signatureDate>2019-05-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
