<?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>0001225207</rptOwnerCik>
            <rptOwnerName>LEIDEL PETER A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>410 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>19TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20000</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>896915</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>896915</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1111111</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrant</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>7.20</value>
                <footnoteId id="F6"/>
                <footnoteId id="F7"/>
            </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="F6"/>
                    <footnoteId id="F7"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </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="F6"/>
                    <footnoteId id="F7"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>408334</value>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On March 15, 2017, Carbon Natural Gas Company (the &quot;Issuer&quot;) effected a one for twenty reverse stock split of the Issuer's issued and outstanding common stock, as reported on the Current Report on Form 8-K filed by the Issuer with the SEC on March 16, 2017.</footnote>
        <footnote id="F2">These securities are owned directly by Yorktown Energy Partners V, L.P. The reporting person is a member and a manager of the general partner of Yorktown Energy Partners V, L.P.</footnote>
        <footnote id="F3">The reporting person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and this report shall not be deemed an admission that the reporting person is the beneficial owner of the securities for Section 16 or any other purpose.</footnote>
        <footnote id="F4">These securities are directly owned by Yorktown Energy Partners VI, L.P. The reporting person is a member and a manager of the general partner of the general partner of Yorktown Energy Partners VI, L.P.</footnote>
        <footnote id="F5">These securities are directly owned by Yorktown Energy Partners IX, L.P. The reporting person is a member and a manager of the general partner of the general partner of Yorktown Energy Partners IX, L.P.</footnote>
        <footnote id="F6">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 the Issuer 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="F7">(continued from Footnote 6) 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>
        <footnote id="F8">These securities are directly owned by Yorktown XI. The reporting person is a member and a manager of the general partner of the general partner of Yorktown XI.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Peter A. Leidel</signatureName>
        <signatureDate>2017-04-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
