<SUBMISSION>
<ACCESSION-NUMBER>0000916457-17-000058
<TYPE>4
<PUBLIC-DOCUMENT-COUNT>1
<PERIOD>20170510
<FILING-DATE>20170510
<DATE-OF-FILING-DATE-CHANGE>20170510
<ISSUER>
<COMPANY-DATA>
<CONFORMED-NAME>CALPINE CORP
<CIK>0000916457
<ASSIGNED-SIC>4911
<IRS-NUMBER>770212977
<STATE-OF-INCORPORATION>DE
<FISCAL-YEAR-END>1231
</COMPANY-DATA>
<BUSINESS-ADDRESS>
<STREET1>717 TEXAS AVENUE
<STREET2>SUITE 1000
<CITY>HOUSTON
<STATE>TX
<ZIP>77002
<PHONE>7138302000
</BUSINESS-ADDRESS>
<MAIL-ADDRESS>
<STREET1>717 TEXAS AVENUE
<STREET2>SUITE 1000
<CITY>HOUSTON
<STATE>TX
<ZIP>77002
</MAIL-ADDRESS>
</ISSUER>
<REPORTING-OWNER>
<OWNER-DATA>
<CONFORMED-NAME>MILLER W. THADDEUS
<CIK>0001442784
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>001-12079
<FILM-NUMBER>17831110
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>717 TEXAS AVENUE, SUITE 1000
<CITY>HOUSTON
<STATE>TX
<ZIP>77002
</MAIL-ADDRESS>
</REPORTING-OWNER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>wf-form4_149444907463249.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-05-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000916457</issuerCik>
        <issuerName>CALPINE CORP</issuerName>
        <issuerTradingSymbol>CPN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001442784</rptOwnerCik>
            <rptOwnerName>MILLER W. THADDEUS</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CALPINE CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>717 TEXAS AVENUE, SUITE 1000</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77002</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, CLO and Secretary</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-02-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>59622</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $0.001 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>59622.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>59622</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Award of restricted stock units pursuant to Calpine Corporation's 2017 Equity Incentive Plan.  The grant was approved by the Board of Directors on February 15, 2017 contingent upon shareholder approval of the 2017 Equity Incentive Plan. The 2017 Equity Incentive Plan was approved by the Company's shareholders at the 2017 Annual Meeting on May 10, 2017 and became effective as of that date. The award vests in three equal annual installments on the first, second and third anniversary dates of the grant date; provided however, that if Mr. Miller is employed by the Company through December 31, 2017, the award shall vest 100% as of such date. Vested shares will be delivered to the reporting person on the settlement date unless the Company elects to settle the restricted stock units in cash or a combination of shares and cash, at the Company's discretion.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>W. Thaddeus Miller</signatureName>
        <signatureDate>2017-05-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
