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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-11-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001401708</issuerCik>
        <issuerName>NanoString Technologies Inc</issuerName>
        <issuerTradingSymbol>NSTG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001134570</rptOwnerCik>
            <rptOwnerName>WAITE CHARLES P JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O OVP VENTURE PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>11023 NE 116TH STREET</rptOwnerStreet2>
            <rptOwnerCity>KIRKLAND</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98034</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-11-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>588024</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.25</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1707</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">375,340 of these shares were sold by OVP Venture Partners VI, L.P., 211,915 of these shares were sold by OVP Venture Partners VII, L.P., and 769 of these shares were sold by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F2">OVMC VI, LLC serves as the general partner of OVP Venture Partners VI, L.P. Charles P. Waite, Jr. is a managing member of OVMC VI, LLC and shares voting and investment power over the shares held by OVP Venture Partners VI, L.P. Charles P. Waite, Jr. is also a managing member of OVMC VII, LLC, the general partner of OVP Venture Partners VII, L.P. and OVP VII Entrepreneurs Fund, L.P., and shares voting and investment power over the shares held by OVP Venture Partners VII, L.P. and OVP VII Entrepreneurs Fund, L.P. Mr. Waite, the other managing members of OVMC VI, LLC and OVMC VII, LLC, and each of the aforementioned entities disclaim beneficial ownership of the reported securities except to the extent of any pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Barbara A. Mery, Attorney-in-fact</signatureName>
        <signatureDate>2016-11-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
