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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-12-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001372612</issuerCik>
        <issuerName>BOX INC</issuerName>
        <issuerTradingSymbol>BOX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001312964</rptOwnerCik>
            <rptOwnerName>Draper Fisher Jurvetson Fund VIII L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DRAPER FISHER JURVETSON</rptOwnerStreet1>
            <rptOwnerStreet2>2882 SAND HILL ROAD, SUITE 150</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>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001385453</rptOwnerCik>
            <rptOwnerName>DRAPER FISHER JURVETSON GROWTH FUND 2006 LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DRAPER FISHER JURVETSON</rptOwnerStreet1>
            <rptOwnerStreet2>2882 SAND HILL ROAD, SUITE 150</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>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001375505</rptOwnerCik>
            <rptOwnerName>DRAPER FISHER JURVETION PARTNERS GROWTH FUND 2006 LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DRAPER FISHER JURVETSON</rptOwnerStreet1>
            <rptOwnerStreet2>2882 SAND HILL ROAD, SUITE 150</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>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-20</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>200</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Bu Fund VIII Partners</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents a pro rata in-kind distribution of Class A Common Stock of the Issuer by Draper Fisher Jurvetson Fund VIII Partners, L.P. (Fund VIII Partners) to its partners or members.</footnote>
        <footnote id="F2">The General Partner of Draper Associates, L.P. (DALP) is Draper Associates, Inc. which is controlled by its President and majority shareholder, Timothy C. Draper. DALP invests lockstep alongside Draper Fisher Jurvetson Fund VIII, L.P. (Fund VIII) and Draper Fisher Jurvetson Fund IX, L.P. (Fund IX).</footnote>
        <footnote id="F3">Timothy C. Draper, John H.N. Fisher and Stephen T. Jurvetson are managing directors of the general partner entities of Fund VIII and Fund IX that directly hold shares and as such they may be deemed to have voting and investment power with respect to such shares. Draper Fisher Jurvetson Partners VIII, LLC (Partners VIII) invests lockstep alongside Fund VIII. Draper Fisher Jurvetson Partners IX, LLC (Partners IX) invests lockstep alongside Fund IX. The managing members of Partners VIII and Partners IX are Timothy C. Draper, John H.N. Fisher and Stephen T. Jurvetson. These individuals disclaim beneficial ownership of these shares except to the extent of their pecuniary interest therein.</footnote>
        <footnote id="F4">John H.N. Fisher, Barry M. Schuler and Mark W. Bailey are managing directors of the general partner entities of Draper Fisher Jurvetson Growth Fund 2006, L.P. (Growth Fund) that directly hold shares and as such they may be deemed to have voting and investment power with respect to such shares.  Draper Fisher Jurvetson Partners Growth Fund 2006, LLC (Growth Partners) invests lockstep alongside Growth Fund.  The managing members of Growth Partners are John H.N. Fisher, Barry M. Schuler, Mark W. Bailey, Timothy C. Draper and Stephen T. Jurvetson.  These individuals disclaim beneficial ownership of these shares except to the extent of their pecuniary interest therein.</footnote>
        <footnote id="F5">Shares were acquired pursuant to a prior pro rata in-kind distribution of Class A Common Stock of the Issuer by Fund VIII to its partners or members including Fund VIII Partners.</footnote>
    </footnotes>

    <remarks>This report is filed as form 2 of 2 to report related transactions for the following filers:  Draper Fisher Jurvetson Fund VIII, L.P.; Draper Fisher Jurvetson Partners VIII, LLC; Draper Fisher Jurvetson Fund IX, L.P.; Draper Fisher Jurvetson Partners IX, LLC; Draper Associates, L.P.; Timothy Draper; John Fisher; Stephen Jurvetson; Mark Bailey; Barry Schuler; Draper Fisher Jurvetson Growth Fund 2006, L.P.; and Draper Fisher Jurvetson Partners Growth Fund 2006, LLC.</remarks>

    <ownerSignature>
        <signatureName>/s/ John Fisher, Managing Director</signatureName>
        <signatureDate>2016-12-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
