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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2017-02-15</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001687163</rptOwnerCik>
            <rptOwnerName>Yorktown XI Associates LLC</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>
        <derivativeHolding>
            <securityTitle>
                <value>Warrant</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.36</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2017-02-15</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-02-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>30555556</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </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 unreturned capital of Yorktown XI's Class A units of Carbon California Company, LLC, a Delaware limited liability company (&quot;CCC&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 CCC, and additional capital contributions made by Yorktown XI to CCC. 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 CCC in accordance with the formula set forth in the warrant.</footnote>
        <footnote id="F3">These securities are owned directly by Yorktown XI. Yorktown XI Associates LLC (&quot;Yorktown XI Associates&quot;) is the sole general partner of Yorktown XI Company LP, the sole general partner of Yorktown XI.</footnote>
        <footnote id="F4">Yorktown XI Associates disclaims beneficial ownership of these securities except to the extent of its pecuniary interest therein, and this report shall not be deemed an admission that Yorktown XI Associates is the beneficial owner of the securities for Section 16 or any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Yorktown XI Associates LLC, /s/ Peter A. Leidel, Manager</signatureName>
        <signatureDate>2017-02-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
