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<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-09-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001452751</issuerCik>
        <issuerName>Nimble Storage Inc</issuerName>
        <issuerTradingSymbol>NMBL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001219231</rptOwnerCik>
            <rptOwnerName>GOETZ JAMES J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SEQUOIA CAPITAL</rptOwnerStreet1>
            <rptOwnerStreet2>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>189901</value>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                    <value>189900</value>
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            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Sequoia Technology Partners XII, L.P.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
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                    <value>542412</value>
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                    <value>542412</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Sequoia Capital XII Principals Fund, LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
                <value>2015-09-30</value>
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                    <value>5075096</value>
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                    <value>D</value>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Sequoia Capital XII, LP</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
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            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>662701</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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                <sharesOwnedFollowingTransaction>
                    <value>662700</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By SC US GF V Holdings, Ltd.</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
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            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>20203</value>
                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <value>20203</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>186718</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>206921</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
                <value>2015-09-30</value>
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                <transactionFormType>4</transactionFormType>
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            <transactionTimeliness>
                <value></value>
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                <transactionShares>
                    <value>11010</value>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
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                <sharesOwnedFollowingTransaction>
                    <value>217931</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
                <value>2015-09-30</value>
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                <value></value>
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                <transactionShares>
                    <value>172</value>
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                    <value>A</value>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Family Trust</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
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            <transactionTimeliness>
                <value></value>
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                <transactionShares>
                    <value>4720</value>
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                    <footnoteId id="F5"/>
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                    <value>A</value>
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                <sharesOwnedFollowingTransaction>
                    <value>4892</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Family Trust</value>
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                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents a pro rata in-kind distribution of Common Stock of the Issuer to partners, shareholders or members and includes subsequent distributions by general partners or managing members to their respective partners or members.</footnote>
        <footnote id="F2">James J. Goetz is a managing member of SC XII Management, LLC (&quot;SC XII Management&quot;). SC XII Management is the general partner of Sequoia Capital XII, L.P. and Sequoia Technology Partners XII, L.P. and is the managing member of Sequoia Capital XII Principals Fund, LLC. By virtue of these relationships, Mr. Goetz may be deemed to share beneficial ownership of the shares held by Sequoia Capital XII, L.P., Sequoia Technology Partners XII, L.P. and Sequoia Capital XII Principals Fund, LLC. The reporting person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F3">SC US (TTGP), Ltd. (&quot;SC US TTGP&quot;) is the general partner of SCGF V Management, L.P. (&quot;SCGF V Management&quot;), which is the general partner of each of Sequoia Capital U.S. Growth Fund V, L.P. and Sequoia Capital USGF Principals Fund V, L.P. Sequoia Capital U.S. Growth Fund V, L.P. and Sequoia Capital USGF Principals Fund V, L.P. together own 100% of the outstanding ordinary shares of SC US GF V Holdings, Ltd. James J. Goetz is one of the directors of SC US TTGP who exercised voting and investment discretion with respect to the SC US GF V Holdings, Ltd.'s investments.  By virtue of these relationships, Mr. Goetz may be deemed to share beneficial ownership of the shares held by SC US GF V Holdings, Ltd.</footnote>
        <footnote id="F4">(Continued from footnote 3) The reporting person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F5">Represents the receipt of shares of Common Stock of the Issuer by virtue of the pro rata in-kind distributions described in footnote (1) above as follows: (i) 20,203 shares from SC US GF V Holdings, Ltd. to the Reporting Person; (ii) 186,718 shares from Sequoia Capital XII, L.P. to the Reporting Person; (iii) 11,010 shares from Sequoia Capital XII Principals Fund, LLC to the Reporting Person; (iv) 172 shares from SC US GF V Holdings, Ltd. to a family trust; and (v) 4,720 shares from Sequoia Capital XII Principals Fund, LLC to a family trust.</footnote>
        <footnote id="F6">Shares held by a family trust. The Reporting Person may be deemed to beneficially own the shares held by the family trust. The Reporting Person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these securities on this report shall not be deemed an admission that the Reporting Person is the beneficial owner of the reported securities for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By:/s/ Melinda Dunn, by power of attorney for James J. Goetz</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
