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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-02-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000815065</issuerCik>
        <issuerName>STERIS CORP</issuerName>
        <issuerTradingSymbol>STE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001300622</rptOwnerCik>
            <rptOwnerName>Breeden Richard C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BREEDEN CAPITAL MANAGEMENT LLC</rptOwnerStreet1>
            <rptOwnerStreet2>100 NORTHFIELD STREET</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</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 Shares, No Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2012-02-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1198</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.28</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14514</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares, No Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1771068</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to the governing documents of Breeden Partners L.P., Breeden Partners (California) L.P., and Breeden Partners (California) II L.P., (the &quot;Funds&quot;), any profits realized with respect to these shares will be apportioned among the Funds</footnote>
        <footnote id="F2">Pursuant to the governing documents of the Funds, any profits realized with respect to these shares will be apportioned among the Funds.</footnote>
        <footnote id="F3">Richard C. Breeden is the managing member of Breeden Capital Partners LLC, managing member and chairman and chief executive officer of Breeden Capital Management LLC and the Key Principal of Breeden Partners (Cayman) Ltd. Breeden Capital Partners LLC is in turn the general partner of Breeden Partners L.P., Breeden Partners (California) L.P. and Breeden Partners (California) II L.P.</footnote>
        <footnote id="F4">Pursuant to Rule 16a-1(a)(2)(ii)(B) of the Securities Exchange Act of 1934, as amended, Mr. Breeden in his capacity as managing member, as well as chairman and chief executive officer of Breeden Capital Management LLC, may be deemed to be the indirect beneficial owner of the Common Shares owned by the Funds; however, he disclaims beneficial ownership of such shares except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Richard C. Breeden</signatureName>
        <signatureDate>2012-02-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
