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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-04-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000086264</issuerCik>
        <issuerName>Carbon Natural Gas Co</issuerName>
        <issuerTradingSymbol>CRBO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001667954</rptOwnerCik>
            <rptOwnerName>Yorktown Energy Partners XI, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>410 PARK AVENUE, 19TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrant</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>7.20</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-04-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>408334</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2017-04-03</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-04-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>408334</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>408334</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The warrant gives Yorktown Energy Partners XI, L.P. (&quot;Yorktown XI&quot;) the right to purchase a number of shares of common stock of Carbon Natural Gas Company (the &quot;Issuer&quot;) determined, as of the time of exercise, by dividing the aggregate Priority Amount attributable to Yorktown XI's Class A units of Carbon Appalachian Company, LLC, a Delaware limited liability company (&quot;CAC&quot;), then held by Yorktown XI by the exercise price then in effect. The number of shares  of common stock of the Issuer and the exercise price are subject to certain adjustments from time to time as set forth in the warrant, including adjustments upon the subdivision or combination of shares of common stock of the Issuer, payment of dividends by the Issuer, distributions by CAC, and additional capital contributions made by Yorktown XI to CAC. The amounts set forth above represent the number of shares of common stock and the exercise price as of the date of the issuance of the warrant.</footnote>
        <footnote id="F2">(Continued from Footnote 1) In consideration of the exercise of the warrant, Yorktown XI shall transfer and assign to the Issuer a number of Class A units of CAC in accordance with the formula set forth in the warrant.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Yorktown Energy Partners XI, L.P., By: Yorktown XI Company LP, its general partner, By: Yorktown XI Associates LLC, its general partner, /s/ Peter A. Leidel, Manager</signatureName>
        <signatureDate>2017-04-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
