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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-07-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001366969</rptOwnerCik>
            <rptOwnerName>O'Driscoll Rory</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SCALE VENTURE MANAGEMENT III, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>950 TOWER LANE, SUITE 1150</rptOwnerStreet2>
            <rptOwnerCity>FOSTER CITY</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94404</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-07-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>500000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>26.35</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>512362</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14284</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9081</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The shares were sold at prices ranging from $26.35 to $26.49.  The reporting person will provide upon request to the SEC, the issuer or security holder of the issuer, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F2">The shares are held of record by Scale Venture Partners III, L.P. (&quot;SVP III&quot;).  Scale Venture Management III, LLC (&quot;SVM III&quot;), the general partner of SVP III, has sole voting and dispositive power with respect to the shares held by SVP III.  Stacey Bishop, Kate Mitchell, Rory O'Driscoll and Andy Vitus, the managing members of SVM III, share voting and dispositive power with respect to the shares held by SVP III.  The reporting person disclaims beneficial ownership of the reported securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F3">The shares are held of record by Scale Management, LLC (&quot;Scale Management&quot;).  Stacey Bishop, Kate Mitchell, Rory O'Driscoll and Andy Vitus, the managing members of Scale Management, share voting and dispositive power with respect to the shares held by Scale Management. The reporting person disclaims beneficial ownership of the reported securities for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Rory O'Driscoll</signatureName>
        <signatureDate>2018-07-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
