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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-02-25</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001466258</issuerCik>
        <issuerName>Ingersoll-Rand plc</issuerName>
        <issuerTradingSymbol>IR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000928265</rptOwnerCik>
            <rptOwnerName>PELTZ NELSON</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>280 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>41ST FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10017</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001345471</rptOwnerCik>
            <rptOwnerName>TRIAN FUND MANAGEMENT, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>280 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>41ST FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10017</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>less than 10% owner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2014-02-25</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2382</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2382</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11977676</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock units that fully vest on February 25, 2015.</footnote>
        <footnote id="F2">Trian Fund Management, L.P (&quot;Trian Management&quot;) serves as the management company for Trian Partners, L.P. (&quot;Trian Onshore&quot;), Trian Partners Master Fund, L.P. (&quot;Trian Offshore&quot;), Trian Partners Parallel Fund I, L.P. (&quot;Parallel Fund I&quot;), Trian Partners Master Fund (ERISA), L.P., (&quot;Trian ERISA&quot;), Trian Partners Strategic Investment Fund, L.P. (&quot;TPSIF&quot;), Trian Partners Strategic Investment Fund-A, L.P. (&quot;Strategic Fund-A&quot;), Trian Partners Strategic Co-Investment Fund-A, L.P. (&quot;Coinvest Fund-A&quot;), Trian IR Holdco Ltd. (&quot;IR Holdco&quot;), Trian SPV (SUB) VI, L.P. (&quot;SPV VI&quot;) and Trian SPV (SUB) VI-A, L.P. (&quot;SPV VI-A&quot; and collectively, the &quot;Trian Entities&quot;) and as such determines the investment and voting decisions of the Trian Entities with respect to the shares of the Issuer held by them.</footnote>
        <footnote id="F3">(FN 2, contd.) Mr. Peltz is a member of Trian Fund Management GP, LLC, which is the general partner of Trian Management, and therefore is in a position to determine the investment and voting decisions made by Trian Management on behalf of the Trian Entities. Accordingly, Mr. Peltz may be deemed to indirectly beneficially own (as that term is defined in Rule 13d-3 under the Securities Exchange Act of 1934) the shares beneficially owned by the Trian Entities. The Reporting Persons disclaim beneficial ownership of such shares except to the extent of their respective pecuniary interests therein and this report shall not be deemed an admission that the Reporting Persons are the beneficial owner of such securities for purposes of Section 16 or for any other purpose. Mr. Peltz is a director of the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Stacey L. Sayetta, Attorney-in-fact for Nelson Peltz</signatureName>
        <signatureDate>2014-02-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Stacey L. Sayetta, Attorney-in-Fact for Peter W. May, member of the general partner of Trian Fund Management, L.P.</signatureName>
        <signatureDate>2014-02-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
