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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-06-15</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000887730</issuerCik>
        <issuerName>KEMET CORP</issuerName>
        <issuerTradingSymbol>KEM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001275868</rptOwnerCik>
            <rptOwnerName>ROGGE KAREN M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>KEMET CORPORATION, KEMET TOWER</rptOwnerStreet1>
            <rptOwnerStreet2>ONE EAST BROWARD BLVD., 2ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>FORT LAUDERDALE</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33301</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>2020-06-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>27.20</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15881</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-06-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>15881</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>27.20</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to the Agreement and Plan of Merger (the &quot;Merger Agreement&quot;) between the Issuer, Yageo Corporation (&quot;Parent&quot;), and Sky Merger Sub Inc., a wholly-owned subsidiary of Parent (&quot;Sub&quot;), dated November 11, 2019, each issued and outstanding share (a &quot;Share&quot;) of common stock of the Issuer was converted into the right to receive $27.20 per Share in cash (subject to any applicable withholding or other taxes or other amounts required by law to be withheld). On June 15, 2020, the transactions contemplated by the Merger Agreement were consummated, including the merger of Sub with and into the Issuer (the &quot;Merger&quot;), with the Issuer continuing as the surviving corporation following the Merger.</footnote>
        <footnote id="F2">Prior to the Merger, Ms. Rogge served on the Board of Directors of the Issuer (the &quot;Board&quot;) and resigned from the Board upon the effective time of the Merger.</footnote>
        <footnote id="F3">Represents restricted stock units of the Issuer. Pursuant to the Merger Agreement (as defined below), each outstanding restricted stock unit was canceled and entitled the holder to receive in exchange therefor, an amount in cash (subject to any applicable withholding or other taxes or other amounts required by law to be withheld) equal to the product of (i) the total number of shares of common stock subject to such restricted stock unit and (ii) $27.20.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Kurt von Moltke, by power of atty for Karen Rogge</signatureName>
        <signatureDate>2020-06-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
