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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-02-28</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001385867</issuerCik>
        <issuerName>Coupa Software Inc</issuerName>
        <issuerTradingSymbol>COUP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001810548</rptOwnerCik>
            <rptOwnerName>Soni Kanika</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O COUPA SOFTWARE INCORPORATED</rptOwnerStreet1>
            <rptOwnerStreet2>1855 S. GRANT STREET</rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-02-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2470</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>81.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2470</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted stock units (&quot;RSUs&quot;) represent a contingent right to receive one share of common stock, par value $0.0001 per share (&quot;Common Stock&quot;), of Coupa Software Incorporated (the &quot;Company&quot;).</footnote>
        <footnote id="F2">The RSUs were disposed of pursuant to the Agreement and Plan of Merger, dated as of December 11, 2022 (the &quot;Merger Agreement&quot;), by and among Coupa Holdings, LLC (f/k/a Project CS Parent, LLC) (&quot;Parent&quot;), Project CS Merger Sub, Inc. (&quot;Merger Sub&quot;), and the Company. Pursuant to the Merger Agreement, Merger Sub merged with and into the Company (the &quot;Merger&quot;), with the Company surviving the Merger as a wholly owned subsidiary of Parent. At the effective time of the Merger (the &quot;Effective Time&quot;), each RSU that was unexpired and unsettled as of immediately prior to the Effective Time was canceled and converted into the right to receive a cash payment equal to the number of shares of Common Stock subject to such RSU as of immediately prior to the Effective Time, multiplied by the $81.00, without interest, less any applicable withholding taxes.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jon Stueve, Authorized Signatory for: Kanika Soni</signatureName>
        <signatureDate>2023-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
