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<ownershipDocument>

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    <documentType>4</documentType>

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

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001374246</rptOwnerCik>
            <rptOwnerName>SC XII MANAGEMENT LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001367770</rptOwnerCik>
            <rptOwnerName>SEQUOIA CAPITAL XII A DELAWARE L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001380096</rptOwnerCik>
            <rptOwnerName>SEQUOIA TECHNOLOGY PARTNERS XII A DELAWARE L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001447932</rptOwnerCik>
            <rptOwnerName>SEQUOIA CAPITAL XII PRINCIPALS FUND LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001607841</rptOwnerCik>
            <rptOwnerName>SC US (TTGP), LTD.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
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            <isTenPercentOwner>1</isTenPercentOwner>
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    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001552459</rptOwnerCik>
            <rptOwnerName>SCGF V Management, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001552461</rptOwnerCik>
            <rptOwnerName>SC US GF V Holdings, Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001528109</rptOwnerCik>
            <rptOwnerName>SEQUOIA CAPITAL U.S. GROWTH FUND V, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
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            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001528063</rptOwnerCik>
            <rptOwnerName>SEQUOIA CAPITAL USGF PRINCIPALS FUND V, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2800 SAND HILL ROAD, SUITE 101</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>189901</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>189900</value>
                </sharesOwnedFollowingTransaction>
            </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>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>542412</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <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>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5075096</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5075096</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <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>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>662701</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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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"/>
                </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">SC XII Management, LLC (&quot;SC XII Management&quot;) 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. As a result, SC XII Management 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. Each of the reporting persons disclaims beneficial ownership of these securities except to the extent of its 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="F3">SC US (TTGP), Ltd. (&quot;SC US TTGP&quot;) is the general partner of SCGF V Management, L.P. (&quot;GF 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. As a result, SC US TTGP, Sequoia Capital U.S. Growth Fund V, L.P., Sequoia Capital USGF Principals Fund V, L.P. and GF V Management may be deemed to share beneficial ownership of the shares held by SC US GF V Holdings, Ltd. Each of the filing persons disclaims beneficial ownership of these securities except to the extent of its 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>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Managing Member of SC XII Management, LLC</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Managing Member of SC XII Management, LLC, the General Partner of Sequoia Capital XII, L.P.</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Managing Member of SC XII Management, LLC, the General Partner of Sequoia Technology Partners XII, L.P.</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Managing Member of SC XII Management, LLC, the Managing Member of Sequoia Capital XII Principals Fund, LLC</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Director of SC US (TTGP), LTD.</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Director of SC US (TTGP), LTD., the General Partner of SCGF V Management, L.P.</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Melinda Dunn, by POA for James J. Goetz, a Director of SC US(TTGP), LTD., the GP of SCGF V Management, L.P., the GP of Sequoia Capital US Growth Fund V, L.P. &amp; Sequoia Capital USGF Principals Fund V, L.P., the shareholders of SC US GF V Holdings, Ltd.</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Director of SC US (TTGP), LTD., the General Partner of SCGF V Management, L.P., the General Partner of  Sequoia Capital US Growth Fund V, L.P</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Melinda Dunn, by power of attorney for James J. Goetz, a Director of SC US (TTGP), LTD., the General Partner of SCGF V Management, L.P., the General Partner of Sequoia Capital USGF Principals Fund V, L.P.</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
