<?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>0001050572</rptOwnerCik>
            <rptOwnerName>GILLIGAN J KEVIN</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>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                <value>Common Stock</value>
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            <transactionDate>
                <value>2018-08-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>158395</value>
                </transactionShares>
                <transactionPricePerShare>
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                    <value>D</value>
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        </nonDerivativeTransaction>
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    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
            <conversionOrExercisePrice>
                <value>65.40</value>
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                </transactionShares>
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            <expirationDate>
                <value>2025-02-18</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>33925</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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            <transactionTimeliness>
                <value></value>
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                <transactionShares>
                    <value>67786</value>
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            <expirationDate>
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            </expirationDate>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                <underlyingSecurityShares>
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        <derivativeTransaction>
            <securityTitle>
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            <conversionOrExercisePrice>
                <value>76.70</value>
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            <transactionDate>
                <value>2018-08-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>40307</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F5"/>
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            <expirationDate>
                <value>2027-02-27</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>40307</value>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
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    </derivativeTable>

    <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 25,508 restricted stock unit awards to acquire common stock of Capella (&quot;Capella RSUs&quot;), 15,577 of which were due to vest on February 22, 2019 and 9,931 of which were due to vest on February 27, 2020. Pursuant to the Merger Agreement, each Capella RSU was disposed of in exchange for a number of restricted stock unit awards to acquire common stock of Strategic Education, Inc. (&quot;Strategic RSUs&quot;) based on the Exchange Ratio. The Strategic RSUs will be subject to substantially the same terms and conditions of the Capella RSUs.  No additional consideration was received in connection with the disposition of such securities.</footnote>
        <footnote id="F3">This option provided for vesting in four equal annual installments beginning February 19, 2016, of which 33,925 shares remained unexercised.  Pursuant to the Merger Agreement, each unexercised option was disposed of in exchange for options to acquire a number of Strategic Education, Inc.'s common stock (&quot;Strategic common stock&quot;) shares based on the Exchange Ratio with an exercise price per share of Strategic common stock equal to the exercise price per share of the Capella stock options divided by the Exchange Ratio. No additional consideration was received in connection with the disposition of such securities.</footnote>
        <footnote id="F4">This option provided for vesting in four equal annual installments beginning February 22, 2017, of which 67,786 shares remained unexercised.  Pursuant to the Merger Agreement, each unexercised option was disposed of in exchange for options to acquire a number of Strategic common stock shares based on the Exchange Ratio with an exercise price per share of Strategic common stock equal to the exercise price per share of the Capella stock options divided by the Exchange Ratio. No additional consideration was received in connection with the disposition of such securities.</footnote>
        <footnote id="F5">This option provided for vesting in four equal annual installments beginning February 27, 2018, of which 40,307 shares remained unexercised. Pursuant to the Merger Agreement, each unexercised option was disposed of in exchange for options to acquire a number of Strategic common stock shares based on the Exchange Ratio with an exercise price per share of Strategic common stock equal to the exercise price per share of the Capella stock options divided by the Exchange Ratio. No additional consideration was received in connection with the disposition of such securities.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kelly Jacobus as Attorney-in-Fact for J. Kevin Gilligan</signatureName>
        <signatureDate>2018-08-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
