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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-07-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000749660</issuerCik>
        <issuerName>ICAD INC</issuerName>
        <issuerTradingSymbol>ICAD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001362512</rptOwnerCik>
            <rptOwnerName>Stevens Stacey M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ICAD INC</rptOwnerStreet1>
            <rptOwnerStreet2>98 SPIT BROOK ROAD SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>NASHUA</rptOwnerCity>
            <rptOwnerState>NH</rptOwnerState>
            <rptOwnerZipCode>03062</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>18.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-07-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>25500</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-02-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>25500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>25500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents options to purchase shares of common stock conditionally approved by the Board of Directors, subject to approval of an amendment to the Company's 2016 Stock Incentive Plan by the Company's stockholders, which approval was obtained at the Company's 2021 Annual Meeting of Stockholders held on July 15, 2021</footnote>
        <footnote id="F2">The shares underlying the option vest annually over a three-year period commencing one year from February 15, 2021, the date the award was conditionally approved by the Board of Directors.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Stacey M. Stevens</signatureName>
        <signatureDate>2021-07-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
