<?xml version="1.0"?>

<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-01-09</periodOfReport>


    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000775345</issuerCik>
        <issuerName>UNITED BANCORP INC /MI/</issuerName>
        <issuerTradingSymbol>UBMI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001256693</rptOwnerCik>
            <rptOwnerName>CHADDERDON DALE L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P O BOX 248</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>TECUMSEH</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>49286</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Sr. VP, Secretary &amp; Treasurer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>

        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $0.00 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6425</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>

        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $0.00 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2062</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>

        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $0.00 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>617</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>

    </nonDerivativeTable>

    <derivativeTable>

        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option Right to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>63</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-01-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1800</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>63</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2005-01-09</value>
            </exerciseDate>
            <expirationDate>
                <value>2014-01-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1800</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1800</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>

    </derivativeTable>


    <remarks>Stock option exercisable at one year commencing 01/09/2005.</remarks>

    <ownerSignature>
        <signatureName>Dale L. Chadderdon</signatureName>
        <signatureDate>2004-01-13</signatureDate>
    </ownerSignature>

</ownershipDocument>

