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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2007-05-08</periodOfReport>

    <dateOfOriginalSubmission>2007-05-10</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000714603</issuerCik>
        <issuerName>DST SYSTEMS INC</issuerName>
        <issuerTradingSymbol>DST</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001017403</rptOwnerCik>
            <rptOwnerName>ALLINSON A EDWARD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>STATE STREET BOSTON CORP</rptOwnerStreet1>
            <rptOwnerStreet2>225 FRANKLIN STREET</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02110</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>2007-05-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1658</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>55175</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">On May 10, 2007, the Reporting Person filed a Form 4 reporting a non-employee Director's restricted stock award of 1,658 shares on May 8, 2007.  The total number of shares owned after the transaction should have been reported as 55,175 instead of 56,833.  These over-reported shares were also included in the direct ownership totals on nine subsequent Form 4s filed by the Reporting Person on November 19, 2007, May 13, 2008, May 12, 2009, May 14, 2009, May 17, 2010, February 18, 2011, March 4, 2011, May 10, 2011 and August 10, 2011.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Randall D. Young for A. Edward Allinson by power of attorney</signatureName>
        <signatureDate>2012-02-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
