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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-02-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001832351</issuerCik>
        <issuerName>Fast Radius, Inc.</issuerName>
        <issuerTradingSymbol>FSRD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001907825</rptOwnerCik>
            <rptOwnerName>Rassey Louis</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FAST RADIUS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>113 N. MAY STREET</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60607</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
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                <transactionPricePerShare>
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            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By TRF I Trust</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
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            </securityTitle>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
                <value></value>
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                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By TRF II Trust</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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            </securityTitle>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
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                </transactionShares>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By TRF III Trust</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <value></value>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By TRF IV Trust</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Two Roads Group, LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <exerciseDate>
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            </exerciseDate>
            <expirationDate>
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            <underlyingSecurity>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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        </derivativeTransaction>
        <derivativeTransaction>
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            <deemedExecutionDate></deemedExecutionDate>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
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            <expirationDate>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            </conversionOrExercisePrice>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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        <derivativeTransaction>
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                <transactionPricePerShare>
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            <ownershipNature>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>38878</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>38878</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38878</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Two Roads Group, LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Received pursuant to that certain Agreement and Plan of Merger (&quot;Merger Agreement&quot;), dated as of July 18, 2021, as amended, by and among Issuer, formerly known as ECP Environmental Growth Opportunities Corp., a Delaware corporation (&quot;ENNV&quot;), ENNV Merger Sub Inc., a Delaware corporation and a wholly-owned subsidiary of ENNV, and Fast Radius, Inc., a Delaware corporation (&quot;Legacy Fast Radius&quot;), in exchange for equity interests of Legacy Fast Radius.</footnote>
        <footnote id="F2">The Reporting Person may be deemed to beneficially own the reported securities. The reporting person disclaims beneficial ownership of such securities, except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F3">Includes 15,508 Restricted Stock Units that are vested and subject to future settlement and 22,691 Restricted Stock Units which vest monthly through May of 2025, subject to the Reporting Person's continuous service.</footnote>
        <footnote id="F4">Represents Restricted Stock Units issued by Legacy Fast Radius and assumed by the Issuer on February 4, 2022 as merger consideration under the Merger Agreement.</footnote>
        <footnote id="F5">Includes 744,442 Restricted Stock Units that are vested and subject to future settlement and 550,547 Restricted Stock Units which vest upon the achievement of certain performance metrics related to the valuation of the Issuer.</footnote>
        <footnote id="F6">Includes 841,540 vested Options and 688,535 Options which vest monthly through March of 2023. The Options expire on May 20, 2029, subject to the Reporting Person's continuous service.</footnote>
        <footnote id="F7">Represents Options issued by Legacy Fast Radius and assumed by the Issuer on February 4, 2022 as merger consideration under the Merger Agreement.</footnote>
        <footnote id="F8">Includes 79,663 vested Options and 185,887 Options which vest monthly through April of 2023. The Options expire on May 20, 2029, subject to the Reporting Person's continuous service.</footnote>
        <footnote id="F9">Represents the right to receive shares of the Issuer's Common Stock in two equal tranches, at the time that the Issuer's Common Stock reaches a value of $15.00 and $20.00, respectively, no later than February 4, 2027, based upon the (i) daily volume-weighted average sale price of shares of the Issuer's Common Stock for any 20 trading days within any 30 consecutive trading day period or (ii) the per share consideration received in connection with a change in control.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Louis Rassey</signatureName>
        <signatureDate>2022-02-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
