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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-02-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000019584</issuerCik>
        <issuerName>CHEMED CORP</issuerName>
        <issuerTradingSymbol>CHE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001207134</rptOwnerCik>
            <rptOwnerName>LEE SPENCER S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2500 CHEMED CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>255 EAST 5TH STREET</rptOwnerStreet2>
            <rptOwnerCity>CINCINNATI</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>45202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>executive vice president</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                <value>capital stock</value>
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                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>519</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>515.12</value>
                </transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
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                    <value>24867</value>
                </sharesOwnedFollowingTransaction>
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                <value></value>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
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            <expirationDate>
                <footnoteId id="F5"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>capital stock</value>
                </underlyingSecurityTitle>
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                    <value>257</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                </sharesOwnedFollowingTransaction>
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                    <value>D</value>
                </directOrIndirectOwnership>
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        <derivativeTransaction>
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            <transactionDate>
                <value>2023-02-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>804</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
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                </transactionAcquiredDisposedCode>
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            <exerciseDate>
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            <expirationDate>
                <footnoteId id="F7"/>
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                <underlyingSecurityTitle>
                    <value>capital stock</value>
                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
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                <sharesOwnedFollowingTransaction>
                    <value>2236</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The number of performance share units (&quot;PSUs&quot;) that vested was based on the Company's achieving adjusted earnings per share growth rate for the period January 1, 2020 through December 31, 2022.  The actual performance of 12.67% yielded an award of 200% of target; including the reinvestment of dividends paid during such period, the award is 202% of target.</footnote>
        <footnote id="F2">The number of PSUs that vested was based on the Company's achieving relative total shareholder returns for the period January 1, 2020 through December 31, 2022, compared to a defined peer group of companies.  The Company's performance ranked in the 55.6th percentile of that group, yielding an award of 113.89%; including the reinvestment of dividends paid during such period, the award is 115% of target.</footnote>
        <footnote id="F3">Shares withheld to satisfy tax obligations in connection with vesting of PSUs.</footnote>
        <footnote id="F4">Each PSU reflects the contingent right to receive a variable number of shares of capital stock based on achieving performance goals.  PSUs were settled in shares on their scheduled vesting date as determined by the Compensation Committee.</footnote>
        <footnote id="F5">PSUs awarded February 21, 2020 vest based on achievement of performance targets over a period of January 1, 2020 to December 31, 2022.  The determination of the performance level was to be made by March 15, 2023.</footnote>
        <footnote id="F6">Each performance stock unit represents a contingent right to receive one share of Chemed Capital Stock</footnote>
        <footnote id="F7">Performance share units vest based on the extent to which the Company achieves certain performance targets over a performance period of January 1, 2023 to December 31, 2025.  The determination of the performance level is to be made by March 15, 2026 and earned shares to be delivered thereafter.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Spencer S. Lee</signatureName>
        <signatureDate>2023-02-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
