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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-01-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001490630</issuerCik>
        <issuerName>Rhino Resource Partners LP</issuerName>
        <issuerTradingSymbol>RNO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001048462</rptOwnerCik>
            <rptOwnerName>WEXFORD CAPITAL LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>411 WEST PUTNAM AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 125</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001472112</rptOwnerCik>
            <rptOwnerName>Wexford GP LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LP</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 125</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001001391</rptOwnerCik>
            <rptOwnerName>DAVIDSON CHARLES E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LP</rptOwnerStreet1>
            <rptOwnerStreet2>411 WEST PUTNAM AVE.</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001048485</rptOwnerCik>
            <rptOwnerName>JACOBS JOSEPH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LP</rptOwnerStreet1>
            <rptOwnerStreet2>411 WEST PUTNAM AVENUE, SUITE 125</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001440276</rptOwnerCik>
            <rptOwnerName>Rhino Energy Holdings LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>411 WEST PUTNAM AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 125</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>159216</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.5171</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6010265</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.5171</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>486744</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>140966</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>599631</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.5171</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This form is jointly filed by Wexford Capital LP (&quot;Wexford&quot;), Charles E. Davidson (&quot;Davidson&quot;), Joseph M. Jacobs (&quot;Jacobs&quot;), Wexford GP LLC (&quot;Wexford GP&quot;) and Rhino Energy Holdings LLC (&quot;REH&quot;). The common units shown as beneficially owned by Davidson, Jacobs, Wexford GP and Wexford, reflect common units that were owned of record by REH. Wexford serves as manager for REH and as such may be deemed to share beneficial ownership of the units beneficially owned by REH, but disclaims such beneficial ownership to the extent such beneficial ownership exceeds its pecuniary interest. (*continued under Footnote (2) below).</footnote>
        <footnote id="F2">(*continued from Footnote (1) above) Wexford GP, as the general partner of Wexford, may be deemed to share beneficial ownership of the units beneficially owned by REH, but disclaims such beneficial ownership to the extent such beneficial ownership exceeds its pecuniary interest. Messrs. Davidson and Jacobs, as the controlling persons of Wexford GP, may be deemed to share beneficial ownership of any units beneficially owned by REH for which Wexford serves as manager, but disclaim such beneficial ownership to the extent such beneficial ownership exceeds their pecuniary interest.</footnote>
        <footnote id="F3">Davidson, as the sole managing member of CD Holding Company, LLC and the beneficial owner of Polycomp Trust Company Custodian FBO Charles E. Davidson Roth IRA #044746R owns these units.</footnote>
        <footnote id="F4">Jacobs, individually, and as a member of J Jacobs Holdings LLC owns these units.</footnote>
        <footnote id="F5">Rhino Resource Holdings LLC (&quot;RRH&quot;) used to own the common units reported on this line. Wexford serves as manager for RRH and as such may be deemed to share beneficial ownership of the units beneficially owned by RRH, but disclaims such beneficial ownership to the extent such beneficial ownership exceeds its pecuniary interest. Wexford GP, as the general partner of Wexford, may be deemed to share beneficial ownership of the units beneficially owned by RRH, but disclaims such beneficial ownership to the extent such beneficial ownership exceeds its pecuniary interest. Messrs. Davidson and Jacobs, as the controlling persons of Wexford GP, may be deemed to share beneficial ownership of any units beneficially owned by RRH for which Wexford serves as manager, but disclaim such beneficial ownership to the extent such beneficial ownership exceeds their pecuniary interest.</footnote>
    </footnotes>

    <remarks>The Form 4's filed on January 5, 2016 by the Reporting Persons, Mark D. Zand, Arthur H. Amron and Kenneth A. Rubin were filed in anticipation of a distribution of common units and subordinated units that did not occur.  Therefore, those reported transactions did not in fact occur.</remarks>

    <ownerSignature>
        <signatureName>Wexford Capital LP By: Wexford GP LLC, its General Partner By: Arthur H. Amron, Vice President and Assistant Secretary</signatureName>
        <signatureDate>2016-01-25</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Wexford GP LLC By: Arthur H. Amron, Vice President and Assistant Secretary</signatureName>
        <signatureDate>2016-01-25</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Joseph M. Jacobs</signatureName>
        <signatureDate>2016-01-25</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Charles E. Davidson</signatureName>
        <signatureDate>2016-01-25</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Rhino Energy Holdings LLC By: Arthur Amron, Vice President and Assistant Secretary</signatureName>
        <signatureDate>2016-01-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
