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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-06-29</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001648955</issuerCik>
        <issuerName>Capitol Acquisition Corp. III</issuerName>
        <issuerTradingSymbol>CLAC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001574445</rptOwnerCik>
            <rptOwnerName>Dryden L. Dyson</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAPITOL ACQUISITION CORP. III</rptOwnerStreet1>
            <rptOwnerStreet2>509 7TH STREET, N.W.</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Officer and Director</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-06-29</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1978750</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Capitol Acquisition Founder 3 LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>11.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-06-29</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1912500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2017-07-29</value>
            </exerciseDate>
            <expirationDate>
                <value>2022-06-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1912500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Capitol Acquisition Founder 3 LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On March 19, 2017, Capitol Acquisition Corp. III (the &quot;Issuer&quot;), Capitol Acquisition Holding Company Ltd. (&quot;Holdings&quot;), Capitol Acquisition Merger Sub, Inc., Canyon Holdings (Cayman) L.P. and Canyon Holdings S.a r.l.  entered into an Agreement and Plan of Merger (the &quot;Merger Agreement&quot;), which was amended as of April 7, 2017, pursuant to which, and subject to the terms and conditions thereof, on June 29, 2017 (the &quot;Closing Date&quot;) the Issuer merged with and into Holdings, with Holdings surviving the merger. On the Closing Date, pursuant to the Merger Agreement, and subject to the terms and conditions thereof, at the effective time of the merger, 413,624 shares of common stock of the Issuer were forfeited and the remaining 1,565,126 shares of common stock of the Issuer were disposed of in exchange for the same number of shares in Holdings.</footnote>
        <footnote id="F2">Mr. Dryden is the managing member of Capitol Acquisition Founder 3 LLC.</footnote>
        <footnote id="F3">On the Closing Date, pursuant to the Merger Agreement, and subject to the terms and conditions thereof, at the effective time of the merger, 485,483 of the Warrants were forfeited and the remaining 1,427,017 Warrants were assumed by Holdings in the Merger.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>L. Dyson Dryden</signatureName>
        <signatureDate>2017-06-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
