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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-08-01</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001104349</issuerCik>
        <issuerName>CAPELLA EDUCATION CO</issuerName>
        <issuerTradingSymbol>CPLA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001380345</rptOwnerCik>
            <rptOwnerName>Tukua Darrell R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>225 SOUTH 6TH STREET, 9TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MINNEAPOLIS</rptOwnerCity>
            <rptOwnerState>MN</rptOwnerState>
            <rptOwnerZipCode>55402</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>2018-08-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>9299</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Each share of common stock of Capella Education Company (&quot;Capella&quot;) reported as disposed of herein was cancelled and converted into the right to receive 0.875 shares of Strategic Education, Inc. (the &quot;Exchange Ratio&quot;) at the effective time of the merger pursuant to that certain Agreement and Plan of Merger, dated as of October 29, 2017, by and among Strayer Education, Inc. (which was renamed &quot;Strategic Education, Inc.&quot; on August 1, 2018), Capella and Sarg Sub Inc. (&quot;Merger Sub&quot;), whereby the parties thereto effected the merger of Capella into Merger Sub to become a wholly owned subsidiary of Strayer Education, Inc.(the &quot;Merger&quot;). No additional consideration was received in connection with the disposition of such securities.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kelly Jacobus, Attorney-in-Fact for Darrell R. Tukua</signatureName>
        <signatureDate>2018-08-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
