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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-06-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001384905</issuerCik>
        <issuerName>RingCentral Inc</issuerName>
        <issuerTradingSymbol>RNG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001586695</rptOwnerCik>
            <rptOwnerName>Marlow John H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O RINGCENTRAL, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>20 DAVIS DRIVE</rptOwnerStreet2>
            <rptOwnerCity>BELMONT</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94002</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, CAO &amp; General Counsel</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <footnoteId id="F1"/>
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                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
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                    <value>170207</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                </transactionShares>
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                </transactionShares>
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        <nonDerivativeTransaction>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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            <transactionDate>
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        <nonDerivativeTransaction>
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    </nonDerivativeTable>

    <derivativeTable>
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            <expirationDate>
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                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
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            <ownershipNature>
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        <derivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
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            <transactionDate>
                <value>2019-06-12</value>
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            <transactionTimeliness>
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                <transactionPricePerShare>
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            <expirationDate>
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                </transactionShares>
                <transactionPricePerShare>
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                <footnoteId id="F10"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F10"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F10"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F10"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F10"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F10"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each Share of Class A Common Stock was issued upon conversion of one share of Class B Common Stock.</footnote>
        <footnote id="F2">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by the Reporting Person on December 14, 2017.</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $116.37 to $117.35, inclusive. The Reporting Person undertakes to provide to the issuer, any security holder of the issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in footnotes (3) through (8) to this Form 4.</footnote>
        <footnote id="F4">The price reported in Column 4 is weighted average price. These shares were sold in multiple transactions at prices ranging from $117.37 to $118.28, inclusive.</footnote>
        <footnote id="F5">The price reported in Column 4 is weighted average price. These shares were sold in multiple transactions at prices ranging from $118.51 to $119.00, inclusive.</footnote>
        <footnote id="F6">The price reported in Column 4 is weighted average price. These shares were sold in multiple transactions at prices ranging from $115.73 to $116.47, inclusive.</footnote>
        <footnote id="F7">The price reported in Column 4 is weighted average price. These shares were sold in multiple transactions at prices ranging from $116.78 to $117.76, inclusive.</footnote>
        <footnote id="F8">The price reported in Column 4 is weighted average price. These shares were sold in multiple transactions at prices ranging from $117.80 to $118.77, inclusive.</footnote>
        <footnote id="F9">Options are fully vested and exercisable.</footnote>
        <footnote id="F10">Each share of Class B Common Stock is convertible at any time at the option of the holder into one share of Class A Common Stock and has no expiration date. In addition, each share of Class B Common Stock held by a shareholder will convert automatically into one share of Class A Common Stock upon (i) any transfer of such share (subject to certain exceptions), or (ii) the occurrence of certain other specific instances, including the vote of the holders of the Class B Common Stock, as set forth in the issuer's Amended and Restated Certificate of Incorporation.</footnote>
        <footnote id="F11">Shares held in a trust for the benefit of the Reporting Person's children. The Reporting Person and his spouse are co-trustees of this trust.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Bruce Johnson as Attorney-in-fact for John Marlow</signatureName>
        <signatureDate>2019-06-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
