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Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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MIC-Info: RSA-MD5,RSA,
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 BapIq7YJOdmZROftyi28DQ==

<SEC-DOCUMENT>0001209191-11-007359.txt : 20110207
<SEC-HEADER>0001209191-11-007359.hdr.sgml : 20110207
<ACCEPTANCE-DATETIME>20110207112339
ACCESSION NUMBER:		0001209191-11-007359
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20110204
FILED AS OF DATE:		20110207
DATE AS OF CHANGE:		20110207

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Wold Peter I
		CENTRAL INDEX KEY:			0001398685

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13105
		FILM NUMBER:		11577059

	MAIL ADDRESS:	
		STREET 1:		6803 SOUTH TUCSON WAY
		CITY:			CENTENNIAL
		STATE:			CO
		ZIP:			80112-3924

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			ARCH COAL INC
		CENTRAL INDEX KEY:			0001037676
		STANDARD INDUSTRIAL CLASSIFICATION:	BITUMINOUS COAL & LIGNITE SURFACE MINING [1221]
		IRS NUMBER:				430921172
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		CITY PLACE ONE STE 300
		STREET 2:		ARCH MINERAL CORP
		CITY:			ST LOUIS
		STATE:			MO
		ZIP:			63141
		BUSINESS PHONE:		3149942700

	MAIL ADDRESS:	
		STREET 1:		CITYPLACE ONE SUITE 300
		STREET 2:		ARCH MINERAL CORP
		CITY:			CREVE COEUR
		STATE:			MO
		ZIP:			63141

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	ARCH MINERAL CORP
		DATE OF NAME CHANGE:	19970411
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc4.xml
<DESCRIPTION>FORM 4 SUBMISSION
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-02-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001037676</issuerCik>
        <issuerName>ARCH COAL INC</issuerName>
        <issuerTradingSymbol>ACI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001398685</rptOwnerCik>
            <rptOwnerName>Wold Peter I</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE CITYPLACE DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>ST. LOUIS</rptOwnerCity>
            <rptOwnerState>MO</rptOwnerState>
            <rptOwnerZipCode>63141</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2011-02-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.30</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jon S. Ploetz, Attorney-in-Fact</signatureName>
        <signatureDate>2011-02-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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