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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2009-06-26</periodOfReport>

    <dateOfOriginalSubmission>2009-06-30</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001368582</issuerCik>
        <issuerName>ArcSight Inc</issuerName>
        <issuerTradingSymbol>ARST</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001294775</rptOwnerCik>
            <rptOwnerName>Ramsey Craig</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ARCSIGHT, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>5 RESULTS WAY</rptOwnerStreet2>
            <rptOwnerCity>CUPERTINO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>95014</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>2009-06-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>70000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.0911</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1126182</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote 2</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2009-06-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>33000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.0437</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1093182</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote 4</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents a weighted average sales price per share. The prices actually received ranged from $16.78 to $17.30. The reporting person has provided to the issuer, and will provide to the SEC staff or any security holder of the issuer, information regarding the number of shares sold at each price within the range.</footnote>
        <footnote id="F2">Represents 725,062 shares held by the reporting person, 234,090 shares held by the reporting person and spouse, together, and 167,030 shares held by the reporting person's spouse.</footnote>
        <footnote id="F3">Represents a weighted average sales price per share. The prices actually received ranged from $17.97 to $18.17. The reporting person has provided to the issuer, and will provide to the SEC staff or any security holder of the issuer, information regarding the number of shares sold at each price within the range.</footnote>
        <footnote id="F4">Represents 725,062 shares held by the reporting person, 201,090 shares held by the reporting person and spouse, together, and 167,030 shares held by the reporting person's spouse.</footnote>
    </footnotes>

    <remarks>Amends and restates in its entirety the Form 4 filed June 30, 2009 to amend the transaction date for the second transaction provided in column 2 of Table I.</remarks>

    <ownerSignature>
        <signatureName>/s/ Tram T. Phi as attorney-in-fact
for Craig Ramsey</signatureName>
        <signatureDate>2009-06-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
