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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-03-22</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001431443</rptOwnerCik>
            <rptOwnerName>Clarus Lifesciences II, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLARUS VENTURES,</rptOwnerStreet1>
            <rptOwnerStreet2>101 MAIN STREET, SUITE 1210</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02142</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001431439</rptOwnerCik>
            <rptOwnerName>Clarus Ventures II GP, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLARUS VENTURES</rptOwnerStreet1>
            <rptOwnerStreet2>101 MAIN STREET, SUITE 1210</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02142</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001762201</rptOwnerCik>
            <rptOwnerName>Blackstone Clarus II L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BLACKSTONE GROUP L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>345 PARK AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10154</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001484870</rptOwnerCik>
            <rptOwnerName>Blackstone Holdings II L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BLACKSTONE GROUP L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>345 PARK AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10154</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001464695</rptOwnerCik>
            <rptOwnerName>Blackstone Holdings I/II GP Inc</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BLACKSTONE GROUP L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>345 PARK AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10154</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001393818</rptOwnerCik>
            <rptOwnerName>Blackstone Group L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>345 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10154</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001404071</rptOwnerCik>
            <rptOwnerName>Blackstone Group Management L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BLACKSTONE GROUP L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>345 PARK AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10154</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001070844</rptOwnerCik>
            <rptOwnerName>SCHWARZMAN STEPHEN A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BLACKSTONE GROUP L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>345 PARK AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10154</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-03-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2000000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.62</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2036025</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This amount represents the $23.00 public offering price per share of common stock, par value $0.0001 per share, of NanoString Technologies, Inc. (the &quot;Issuer&quot;), less the underwriting discount of $1.38 per share.</footnote>
        <footnote id="F2">These securities are held directly by Clarus Lifesciences II, L.P. (&quot;Clarus II&quot;). Clarus Ventures II GP, L.P. (&quot;Clarus II GP&quot;) is the sole general partner of Clarus II. Blackstone Clarus II L.L.C. is the sole general partner of Clarus GP. The sole member of Blackstone Clarus II L.L.C. is Blackstone Holdings II L.P. The sole general partner of Blackstone Holdings II L.P. is Blackstone Holdings I/II GP Inc. The controlling shareholder of Blackstone Holdings I/II GP Inc. is The Blackstone Group L.P. The sole general partner of The Blackstone Group L.P. is Blackstone Group Management L.L.C. Blackstone Group Management L.L.C. is wholly-owned by Blackstone's senior managing directors and controlled by its founder, Stephen A. Schwarzman.</footnote>
        <footnote id="F3">Information with respect to each of the Reporting Persons is given solely by such Reporting Person, and no Reporting Person has responsibility for the accuracy or completeness of information supplied by another Reporting Person.</footnote>
        <footnote id="F4">Each of the Reporting Persons (other than Clarus II) disclaims beneficial ownership of the securities held by Clarus II, except to the extent of such Reporting Person's pecuniary interest therein, and, pursuant to Rule 16a-1(a)(4) under the Securities Exchange Act of 1934, each of the Reporting Persons (other than Clarus II) states that the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all of the reported securities for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>CLARUS LIFESCIENCES II, L.P., By: Clarus Ventures II GP, L.P., its GP, By: Blackstone Clarus II L.L.C., its GP, By: Blackstone Holdings II L.P., its managing member, By: Blackstone Holdings I/II GP Inc., its GP, By: /s/ John G. Finley, Title: CLO</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CLARUS VENTURES II GP, L.P., By: Blackstone Clarus II L.L.C., its GP, By: Blackstone Holdings II L.P., its managing member, By: Blackstone Holdings I/II GP Inc., its GP, By: /s/ John G. Finley, Name: John G. Finley, Title: Chief Legal Officer</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>BLACKSTONE CLARUS II L.L.C., By: Blackstone Holdings II L.P., its managing member, By: Blackstone Holdings I/II GP Inc., its general partner, By: /s/ John G. Finley, Name: John G. Finley, Title: Chief Legal Officer</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>BLACKSTONE HOLDINGS II L.P., By: Blackstone Holdings I/II GP Inc., its general partner, By: /s/ John G. Finley, Name: John G. Finley, Title: Chief Legal Officer</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>BLACKSTONE HOLDINGS I/II GP INC., By: /s/ John G. Finley, Name: John G. Finley, Title: Chief Legal Officer</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>THE BLACKSTONE GROUP L.P., By: Blackstone Group Management L.L.C., its general partner, By: /s/ John G. Finley, Name: John G. Finley, Title: Chief Legal Officer</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>BLACKSTONE GROUP MANAGEMENT L.L.C., By: /s/ John G. Finley,  Name: John G. Finley, Title: Chief Legal Officer</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Stephen A. Schwarzman</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
