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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-12-31</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>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>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>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>1</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>2012-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1608945</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6010265</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19740</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <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="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>140966</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F7"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>603647</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Subordinated Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-12-31</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2013-01-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2301542</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Units</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2301542</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8597487</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>Subordinated Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Units</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>696268</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>696268</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Subordinated Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Units</value>
                    <footnoteId id="F9"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>201642</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>201642</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F7"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Subordinated Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Units</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>863509</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>863509</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Rhino Energy Holdings LLC (&quot;REH&quot;) made an in-kind distribution of 1,608,945 common units and 2,301,542 subordinated units to certain of its investors.</footnote>
        <footnote id="F2">This form is jointly filed by Wexford Capital LP (&quot;Wexford&quot;), Charles E. Davidson (&quot;Davidson&quot;), Joseph M. Jacobs (&quot;Jacobs&quot;) and Wexford GP LLC (&quot;Wexford GP&quot;). The common units shown as beneficially owned by Davidson, Jacobs, Wexford GP and Wexford, reflect common units 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 (3) below).</footnote>
        <footnote id="F3">(*continued from Footnote (2) 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="F4">Under the Rhino Long-Term Incentive Plan (the &quot;Plan&quot;), on October 5, 2010, on behalf of the services of Joseph M. Jacobs, Mark D. Zand, Jay L. Maymudes, Arthur H. Amron and Kenneth A. Rubin, as directors of Rhino GP LLC, the general partner of the Partnership, Wexford was granted 6,100 common units subject to the terms and conditions set forth in the Plan.  These common units became fully vested as of July 1, 2011. On November 3, 2011, Wexford on behalf of the services of these same individual directors was granted an additional 6,130 common units subject to the terms and conditions set forth in the Plan. These common units became fully vested as of July 1, 2012.  On October 31, 2012, Wexford on behalf of the services of these same individual directors was granted an additional 7,510 common units subject to the terms and conditions set forth in the Plan. (*continued under Footnote (5) below).</footnote>
        <footnote id="F5">(*continued from Footnote (4) above) These additional units are subject to vesting as follows: 1,880 units vested on the grant date, 1,880 units vested on January 1, 2013, 1,875 units will vest on April 1, 2013 and 1,875 units will vest on July 1, 2013.</footnote>
        <footnote id="F6">Davidson, as the sole managing member of CD Holding Company, LLC and the beneficial owner of Charles E. Davidson Roth IRA #4 JPMC, received an in-kind distribution of 281,028 common units and 402,007 subordinated units.</footnote>
        <footnote id="F7">Jacobs, individually, and as a member of Jacobs Holdings LLC and the beneficial owner of Joseph Jacobs Roth IRA 7 received an in-kind distribution of 91,412 common units and 130,757 subordinated units.</footnote>
        <footnote id="F8">Rhino Resource Holdings LLC (&quot;RRH&quot;) received an in-kind distribution of 237,132 common units and 339,216 subordinated units. 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 its pecuniary interest.</footnote>
        <footnote id="F9">The subordinated units will convert into common units on a one-for-one basis at the times set forth in, and subject to the terms and condidtions of, the issuer's Partnership Agreement.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Wexford Capital LP By: Wexford GP LLC, its General Partner By: Arthur H. Amron, Vice President and Assistant Secretary</signatureName>
        <signatureDate>2013-01-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Wexford GP LLC By: Arthur H. Amron, Vice President and Assistant Secretary</signatureName>
        <signatureDate>2013-01-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Joseph M. Jacobs</signatureName>
        <signatureDate>2013-01-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Charles E. Davidson</signatureName>
        <signatureDate>2013-01-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
