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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-03-24</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>1616 EASTLAKE AVE. E., SUITE 208</rptOwnerStreet2>
            <rptOwnerCity>SEATTLE</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98102</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>2016-03-24</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>500000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1037480</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-03-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1707</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1707</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Pro rata distribution without consideration by OVP Venture Partners VI, L.P., OVP Venture Partners VII, L.P., OVMC VI, L.L.C. and OVMC VII, L.L.C. to their respective limited partners and members.</footnote>
        <footnote id="F2">738,775 of these shares are owned by OVP Venture Partners VI, L.P., 297,221 of these shares are owned by OVP Venture Partners VII, L.P., and 1,484 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F3">OVMC VI, L.L.C. serves as the general partner of OVP Venture Partners VI, L.P. Charles P. Waite, Jr. is a managing member of OVMC VI, L.L.C. 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, L.L.C., 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, L.L.C. and OVMC VII, L.L.C., and each of the aforementioned entities disclaim beneficial ownership of the reported securities except to the extent of any pecuniary interest therein.</footnote>
        <footnote id="F4">Acquisition by the reporting person pursuant to a pro rata distribution without consideration from each of OVMC VI, L.L.C and OVMC VII, L.L.C., of which the reporting person is a member.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Barbara A. Mery, Attorney-in-fact</signatureName>
        <signatureDate>2016-03-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
