<?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>0001249449</rptOwnerCik>
            <rptOwnerName>LOMAX MICHAEL L</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>10021</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </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>
        <footnote id="F2">Includes 6,519 deferred stock units to be settled in Capella common stock. The deferred stock units were fully vested prior to the closing of the Merger. Pursuant to the Merger Agreement, each deferred stock unit was disposed of in exchange for a number of deferred stock units to be settled in common stock of Strategic Education, Inc. based on the Exchange Ratio. The deferred stock units will be subject to substantially the same terms and conditions of the Capella deferred stock units. 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 Michael L. Lomax</signatureName>
        <signatureDate>2018-08-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
