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

    <schemaVersion>X0306</schemaVersion>

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    <periodOfReport>2016-07-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001327467</issuerCik>
        <issuerName>Celator Pharmaceuticals Inc</issuerName>
        <issuerTradingSymbol>CPXX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001566617</rptOwnerCik>
            <rptOwnerName>Jackson Scott Thomas</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CELATOR PHARMACEUTICALS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>200 PRINCETONSOUTH CORP. CENTER, STE 180</rptOwnerStreet2>
            <rptOwnerCity>EWING</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>08628</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
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                </transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
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                </directOrIndirectOwnership>
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        </nonDerivativeTransaction>
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    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
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            <exerciseDate>
                <footnoteId id="F1"/>
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            <expirationDate>
                <value>2017-12-04</value>
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                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <transactionCode>M</transactionCode>
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                <transactionPricePerShare>
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            <expirationDate>
                <value>2019-03-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>117064</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
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                <value>3.116</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-07-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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            <exerciseDate>
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            <expirationDate>
                <value>2023-06-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
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                </underlyingSecurityShares>
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                <sharesOwnedFollowingTransaction>
                    <value>333724</value>
                </sharesOwnedFollowingTransaction>
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    </derivativeTable>

    <footnotes>
        <footnote id="F1">This option is vested in full.</footnote>
        <footnote id="F2">This option is vested in full.</footnote>
        <footnote id="F3">This option vests as follows: (i) 107,500 options vest on June 3, 2014; and (ii) 322,500 options vest in twelve consecutive quarterly installments of 26,875 shares, each on the 3rd day of the respective month beginning September 3, 2014 and continuing through June 3, 2017.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Scott T. Jackson</signatureName>
        <signatureDate>2016-07-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
