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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-04-25</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001636286</issuerCik>
        <issuerName>People's Utah Bancorp</issuerName>
        <issuerTradingSymbol>PUB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001640731</rptOwnerCik>
            <rptOwnerName>Fairclough, Jr. Fred W.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PEOPLE?S UTAH BANCORP</rptOwnerStreet1>
            <rptOwnerStreet2>1 EAST MAIN STREET</rptOwnerStreet2>
            <rptOwnerCity>AMERICAN FORK</rptOwnerCity>
            <rptOwnerState>UT</rptOwnerState>
            <rptOwnerZipCode>84003</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2018-04-25</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>32.0375</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>370676</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to a 10b5-1 plan, the price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $31.90 to $32.15. The reporting person undertakes to provide People's Utah Bancorp, any security holder of People's Utah Bancorp, or the staff of the Securities and Exchange Commission, on request, full information regarding the number of shares sold at each separate price within the ranges set forth in this footnote to this Form 4.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Fred W. Fairclough, Jr. by Jonathan T Allen, Attorney in Fact</signatureName>
        <signatureDate>2018-04-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
