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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-05-02</periodOfReport>

    <issuer>
        <issuerCik>0001141982</issuerCik>
        <issuerName>Cooper Industries plc</issuerName>
        <issuerTradingSymbol>CBE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001237682</rptOwnerCik>
            <rptOwnerName>POSTL JAMES J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>700 LOUISIANA, SUITE 2445</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77002</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2011-05-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2993</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>45401</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Awarded pursuant to the Amended and Restated Director's Stock Plan.</footnote>
        <footnote id="F2">Includes 539 unissued shares for dividend equivalents credited pursuant to the Amended and Restated Directors' Stock Plan and includes 257 unissued shares for dividend equivalents credited pursuant to the Directors' Retainer Fee Stock Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Attorney-in-fact</signatureName>
        <signatureDate>2011-05-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
