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

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-05-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001820630</issuerCik>
        <issuerName>Proterra Inc</issuerName>
        <issuerTradingSymbol>PTRA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001888690</rptOwnerCik>
            <rptOwnerName>Bailey Christopher L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PROTERRA INC</rptOwnerStreet1>
            <rptOwnerStreet2>1815 ROLLINS ROAD</rptOwnerStreet2>
            <rptOwnerCity>BURLNGAME</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94010</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President, Powered &amp; Energy</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-05-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3742</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.1433</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>480771</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The sale reported in this Form 4 represents a nondiscretionary sale of shares required to be sold by the Reporting Person pursuant to sell to cover transactions to satisfy tax withholding obligations in connection with the vesting and settlement of restricted stock units.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Christopher L. Bailey, by /s/ Ron A. Metzger, Attorney-in-Fact</signatureName>
        <signatureDate>2023-05-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
