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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2023-09-01</periodOfReport>

    <dateOfOriginalSubmission>2023-09-06</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000889900</issuerCik>
        <issuerName>PATTERSON UTI ENERGY INC</issuerName>
        <issuerTradingSymbol>PTEN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001702981</rptOwnerCik>
            <rptOwnerName>STEWART JAMES CARL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>10713 W SAM HOUSTON PKWY N</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 800</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77064</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2023-09-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>96235</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>96235</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2023-09-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1339754</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1339754</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By JCS Partners LP</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>20.79</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-09-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>134682</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2023-09-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $.01 par value per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>134682</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>134682</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>18.85</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-09-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>23092</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2023-09-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $.01 par value per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>23092</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23092</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This Form 4 reports securities acquired in connection with the mergers (the &quot;Mergers&quot;) contemplated by that certain Agreement and Plan of Merger (as amended, the &quot;Merger Agreement&quot;), dated as of June 14, 2023, by and among Patterson-UTI Energy, Inc. (the &quot;Issuer&quot;), certain subsidiaries of the Issuer, and NexTier Oilfield Solutions Inc. (&quot;NexTier&quot;). On September 1, 2023, as a result of the Mergers contemplated by the Merger Agreement, at the Effective Time (as defined in the Merger Agreement), each outstanding share of common stock of NexTier was converted automatically into the right to receive 0.7520 (the &quot;Exchange Ratio&quot;) shares of common stock of the Issuer, with cash paid in lieu of the issuance of any fractional shares of the Issuer's common stock.</footnote>
        <footnote id="F2">The shares of the Issuer's common stock reported above were acquired by the Reporting Person in respect of the shares of common stock of NexTier owned by the Reporting Person immediately prior to the Effective Time. On the trading day immediately prior to the Effective Time, the closing price of the Issuer's common stock was $14.14 per share and the closing price of NexTier's common stock was $10.61 per share.</footnote>
        <footnote id="F3">Held by JCS Partners LP, a limited partnership over which the reporting person exercises ownership and control.</footnote>
        <footnote id="F4">These fully vested stock options were acquired by the Reporting Person in the Mergers in exchange for stock options to purchase shares of common stock of NexTier for $15.63 per share held by the Reporting Person immediately prior to the Effective Time based on the Exchange Ratio.</footnote>
        <footnote id="F5">These fully vested stock options were acquired by the Reporting Person in the Mergers in exchange for stock options to purchase shares of common stock of NexTier for $14.17 per share held by the Reporting Person immediately prior to the Effective Time based on the Exchange Ratio.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By Forrest Robinson pursuant to a limited power of attorney filed with the SEC on 09/06/2023 /s/Forrest Robinson</signatureName>
        <signatureDate>2023-09-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
