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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-08-21</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001254583</rptOwnerCik>
            <rptOwnerName>MITAROTONDA JAMES A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BARINGTON CAPITAL GROUP, L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>888 SEVENTH AVENUE, 17TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-08-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>34910</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-08-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>322678</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.00</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Barington Companies Equity Partners, L.P</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of pursuant to the merger agreement (the &quot;Merger Agreement&quot;) between the issuer, LyondellBasell Industries N.V and LYB Americas Holdco Inc.  In addition to the cash consideration, each shareholder will also receive one contingent value right (&quot;CVR&quot;) per share or, with respect to equity awards, per share underlying each such equity award. Each CVR will represent the right to receive contingent cash payments from certain net proceeds, if any are recovered, relating to claims arising from the issuer's acquisition of its Citadel subsidiary or the acquisition by Citadel's subsidiary, the Matrixx Group, Incorporated of its Lucent subsidiary, including from certain ongoing litigation against the former owners of the issuer's Citadel subsidiary and the former owners of A. Schulman's Lucent subsidiary and the related government investigations.  Reporting person will receive 34,910 CVRs.</footnote>
        <footnote id="F2">In addition to the cash consideration, 322,678 CVRs were issued to Barington Companies Equity Partners, L.P.</footnote>
        <footnote id="F3">The Reporting Person's relationship to Barington Companies Equity Partners, L.P. is described in this footnote. The Reporting Person is the sole stockholder and director of LNA Capital Corp., which is the general partner of Barington Capital Group, L.P., which is the majority member of Barington Companies Investors, LLC. Barington Companies Investors, LLC is the general partner of Barington Companies Equity Partners, L.P.</footnote>
        <footnote id="F4">The Reporting Person disclaims beneficial ownership of these securities, except to the extent of his pecuniary interest therein, and this report shall not be deemed to be an admission that the Reporting Person is the beneficial owner of these securities for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ James A. Mitarotonda</signatureName>
        <signatureDate>2018-08-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
