<SEC-DOCUMENT>0001675149-18-000035.txt : 20180201
<SEC-HEADER>0001675149-18-000035.hdr.sgml : 20180201
<ACCEPTANCE-DATETIME>20180201165932
ACCESSION NUMBER:		0001675149-18-000035
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20180131
FILED AS OF DATE:		20180201
DATE AS OF CHANGE:		20180201

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Sigurdsson Tomas Mar
		CENTRAL INDEX KEY:			0001687322

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-37816
		FILM NUMBER:		18567550

	MAIL ADDRESS:	
		STREET 1:		201 ISABELLA STREET, SUITE 500
		CITY:			PITTSBURGH
		STATE:			PA
		ZIP:			15212

	FORMER NAME:	
		FORMER CONFORMED NAME:	Sigurdsson Thomas Mar
		DATE OF NAME CHANGE:	20161012

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Alcoa Corp
		CENTRAL INDEX KEY:			0001675149
		STANDARD INDUSTRIAL CLASSIFICATION:	PRIMARY PRODUCTION OF ALUMINUM [3334]
		IRS NUMBER:				811789115
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		201 ISABELLA STREET
		STREET 2:		SUITE 500
		CITY:			PITTSBURGH
		STATE:			PA
		ZIP:			15212
		BUSINESS PHONE:		412-315-2900

	MAIL ADDRESS:	
		STREET 1:		201 ISABELLA STREET
		STREET 2:		SUITE 500
		CITY:			PITTSBURGH
		STATE:			PA
		ZIP:			15212

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	Alcoa Upstream Corp
		DATE OF NAME CHANGE:	20160520
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>edgar.xml
<DESCRIPTION>PRIMARY DOCUMENT
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-01-31</periodOfReport>

    <issuer>
        <issuerCik>0001675149</issuerCik>
        <issuerName>Alcoa Corp</issuerName>
        <issuerTradingSymbol>AA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001687322</rptOwnerCik>
            <rptOwnerName>Sigurdsson Tomas Mar</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>201 ISABELLA STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>PITTSBURGH,</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>15212</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Exec VP and COO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.3687</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46832</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in column 4 is a weighted average price.  The shares were sold in multiple transactions at prices ranging from $51.3300 - $51.4200.  The reporting person undertakes to provide to Alcoa Corp., any security holder of Alcoa Corp., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each price within the range set forth in this footnote.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Marissa Earnest (Assistant Secretary), by power of attorney</signatureName>
        <signatureDate>2018-02-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
