<SEC-DOCUMENT>0000091142-21-000115.txt : 20210714
<SEC-HEADER>0000091142-21-000115.hdr.sgml : 20210714
<ACCEPTANCE-DATETIME>20210714150523
ACCESSION NUMBER:		0000091142-21-000115
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20210712
FILED AS OF DATE:		20210714
DATE AS OF CHANGE:		20210714

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			WULF GENE C
		CENTRAL INDEX KEY:			0001215484

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-00475
		FILM NUMBER:		211090088

	MAIL ADDRESS:	
		STREET 1:		A. O. SMITH CORPORATION
		STREET 2:		11270 WEST PARK PLACE
		CITY:			MILWAUKEE
		STATE:			WI
		ZIP:			53224

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			SMITH A O CORP
		CENTRAL INDEX KEY:			0000091142
		STANDARD INDUSTRIAL CLASSIFICATION:	HOUSEHOLD APPLIANCES [3630]
		IRS NUMBER:				390619790
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		11270 WEST PARK PLACE
		CITY:			MILWAUKEE
		STATE:			WI
		ZIP:			53224
		BUSINESS PHONE:		4143594000

	MAIL ADDRESS:	
		STREET 1:		11270 WEST PARK PLACE
		CITY:			MILWAUKEE
		STATE:			WI
		ZIP:			53224
</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>2021-07-12</periodOfReport>

    <issuer>
        <issuerCik>0000091142</issuerCik>
        <issuerName>SMITH A O CORP</issuerName>
        <issuerTradingSymbol>AOS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001215484</rptOwnerCik>
            <rptOwnerName>WULF GENE C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>A. O. SMITH CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>11270 WEST PARK PLACE</rptOwnerStreet2>
            <rptOwnerCity>MILWAUKEE</rptOwnerCity>
            <rptOwnerState>WI</rptOwnerState>
            <rptOwnerZipCode>53224</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-07-12</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>142</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>70.855</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>85798</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Payment of retainer in stock under the A. O. Smith Corporation directors' compensation program based on the average of the high and low price of Common Stock on July 12, 2021.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James F. Stern, Attorney-in-Fact for Gene C. Wulf</signatureName>
        <signatureDate>2021-07-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
