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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-09-04</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>2014-09-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>43017</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.144</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1641037</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>2014-09-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>23276</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.144</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1617761</value>
                    <footnoteId id="F4"/>
                </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>2014-09-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>589</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.144</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1617172</value>
                    <footnoteId id="F5"/>
                </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>2014-09-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>60</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.144</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1617112</value>
                    <footnoteId id="F6"/>
                </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>2014-09-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12852</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.2606</value>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1604260</value>
                    <footnoteId id="F8"/>
                </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>2014-09-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6954</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.2606</value>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1597306</value>
                    <footnoteId id="F9"/>
                </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>2014-09-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>176</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.2606</value>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1597130</value>
                    <footnoteId id="F10"/>
                </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>2014-09-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>18</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.2606</value>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1597112</value>
                    <footnoteId id="F11"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The &quot;Amount&quot; and &quot;Price&quot; reported in this Column 4 reflect the aggregate number and weighted-average price, respectively, of shares sold. These shares were sold in multiple transactions at prices ranging from $11.05 to $11.375, inclusive. The reporting person undertakes to provide to the issuer, any security holder of the issuer, or the SEC staff, upon request, full information regarding the number of shares sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F2">1,105,544 of these shares are owned by OVP Venture Partners VI, L.P., 15,794 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 518,097 of these shares are owned by OVP Venture Partners VII, L.P., and 1,602 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F3">OVMC VI, LLC serves as the general partner of OVP Venture Partners VI, L.P. and OVP VI Entrepreneurs Fund, 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. and OVP VI Entrepreneurs Fund, 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>
        <footnote id="F4">1,105,544 of these shares are owned by OVP Venture Partners VI, L.P., 15,794 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 494,821 of these shares are owned by OVP Venture Partners VII, L.P., and 1,602 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F5">1,105,544 of these shares are owned by OVP Venture Partners VI, L.P., 15,205 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 494,821 of these shares are owned by OVP Venture Partners VII, L.P., and 1,602 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F6">1,105,544 of these shares are owned by OVP Venture Partners VI, L.P., 15,205 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 494,821 of these shares are owned by OVP Venture Partners VII, L.P., and 1,542 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F7">The &quot;Amount&quot; and &quot;Price&quot; reported in this Column 4 reflect the aggregate number and weighted-average price, respectively, of shares sold. These shares were sold in multiple transactions at prices ranging from $11.235 to $11.34, inclusive. The reporting person undertakes to provide to the issuer, any security holder of the issuer, or the SEC staff, upon request, full information regarding the number of shares sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F8">1,092,692 of these shares are owned by OVP Venture Partners VI, L.P., 15,205 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 494,821 of these shares are owned by OVP Venture Partners VII, L.P., and 1,542 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F9">1,092,692 of these shares are owned by OVP Venture Partners VI, L.P., 15,205 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 487,867 of these shares are owned by OVP Venture Partners VII, L.P., and 1,542 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F10">1,092,692 of these shares are owned by OVP Venture Partners VI, L.P., 15,029 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 487,867 of these shares are owned by OVP Venture Partners VII, L.P., and 1,542 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
        <footnote id="F11">1,092,692 of these shares are owned by OVP Venture Partners VI, L.P., 15,029 of these shares are owned by OVP VI Entrepreneurs Fund, L.P., 487,867 of these shares are owned by OVP Venture Partners VII, L.P., and 1,524 of these shares are owned by OVP VII Entrepreneurs Fund, L.P.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Barbara A. Mery, Attorney-in-fact</signatureName>
        <signatureDate>2014-09-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
