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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-08-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000087565</issuerCik>
        <issuerName>SCHULMAN A INC</issuerName>
        <issuerTradingSymbol>SHLM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001015029</rptOwnerCik>
            <rptOwnerName>MILLER PEGGY GORDON</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>929 HARVEY DUNN ST.</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BROOKINGS</rptOwnerCity>
            <rptOwnerState>SD</rptOwnerState>
            <rptOwnerZipCode>57006</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>21.32</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-08-04</value>
            </transactionDate>
            <deemedExecutionDate>
                <footnoteId id="F1"/>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>76.24</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.32</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>76.24</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12046.37</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This field is not applicable.</footnote>
        <footnote id="F2">Pursuant to the A. Schulman, Inc. 2002 Equity Incentive Plan, directors may elect to defer all or a portion of their director fees by receiving Phantom Stock Units in lieu of such fees.  The number of Phantom Stock Units received is calculated by dividing the amount of fees deferred by the closing price of the Issuer's Common Stock on the last business day of the preceding calendar year. Phantom Stock Units held by directors are credited with, and additional Phantom Stock Units are issued based on the amount of, dividends paid with respect to the Issuer's Common Stock from time to time.  The Phantom Stock Units reflected in this Report were issued based on dividends paid with respect to the Issuer's Common Stock, which dividends were credited as of the dividend payment date to the Phantom Stock Units held by the Reporting Person.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Dr. Peggy G. Miller, by Laura D. Nemeth as attorney-in-fact</signatureName>
        <signatureDate>2004-08-24</signatureDate>
    </ownerSignature>
</ownershipDocument>

