<SUBMISSION>
<ACCESSION-NUMBER>0000916457-17-000086
<TYPE>4
<PUBLIC-DOCUMENT-COUNT>1
<PERIOD>20170516
<FILING-DATE>20170518
<DATE-OF-FILING-DATE-CHANGE>20170518
<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>Hill Thad
<CIK>0001351761
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>001-12079
<FILM-NUMBER>17856159
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>717 TEXAS AVENUE
<STREET2>SUITE 1000
<CITY>HOUSTON
<STATE>TX
<ZIP>77002
</MAIL-ADDRESS>
</REPORTING-OWNER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>wf-form4_149514900763690.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-05-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001351761</rptOwnerCik>
            <rptOwnerName>Hill Thad</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>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.001 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9677</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>597541</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>12.4</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-05-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>15571</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2020-05-16</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-05-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $0.001 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15571.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15571</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Stock Units</value>
                <footnoteId id="F3"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-05-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6706</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $0.001 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6706.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6706</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Award of restricted stock pursuant to Calpine Corporation's (the &quot;Company&quot;) 2017 Equity Incentive Plan.  The award vests in three equal annual installments on the first, second and third anniversary dates of the grant date.</footnote>
        <footnote id="F2">Granted pursuant to the Company's 2017 Equity Incentive Plan; vesting 100% on May 16, 2020.</footnote>
        <footnote id="F3">Granted pursuant to the Company's 2017 Equity Incentive Plan.  The number of performance share units (&quot;PSUs&quot;) reported represents the &quot;target&quot; number of PSUs that may be earned. Each PSU represents a contingent right to receive 0-150% of the target award. PSUs will vest and be paid in cash (in an amount equal to the product of the number of earned PSUs multiplied by the fair market value of one share of common stock of the Company as of the last trading day of the performance cycle) upon achievement of the specified thresholds of the Company's total shareholder return over the three-year performance period of May 16, 2017 through May 15, 2020, following the Compensation Committee's certification of performance as soon as practicable following completion of the performance period.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ W. Thaddeus Miller by Power of Attorney</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
