<SEC-DOCUMENT>0000091142-22-000041.txt : 20220215
<SEC-HEADER>0000091142-22-000041.hdr.sgml : 20220215
<ACCEPTANCE-DATETIME>20220215151156
ACCESSION NUMBER:		0000091142-22-000041
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20220211
FILED AS OF DATE:		20220215
DATE AS OF CHANGE:		20220215

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Goodwin Wallace E
		CENTRAL INDEX KEY:			0001736083

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-00475
		FILM NUMBER:		22638788

	MAIL ADDRESS:	
		STREET 1:		LOCHINVAR, LLC
		STREET 2:		300 MADDOX SIMPSON PARKWAY
		CITY:			LEBANON
		STATE:			TN
		ZIP:			37090

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>wf-form4_164495590358816.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-02-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001736083</rptOwnerCik>
            <rptOwnerName>Goodwin Wallace E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>LOCHINVAR, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>300 MADDOX SIMPSON PARKWAY</rptOwnerStreet2>
            <rptOwnerCity>LEBANON</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37090</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP; President, Lochinvar, LLC</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-11</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1670</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>71.715</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18550</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-11</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>658</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>71.715</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17892</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>71.715</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-02-11</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1670</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1670.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4465</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The restricted stock units were granted on 02/10/2020 under the A. O. Smith Combined Incentive Compensation Plan, a transaction exempt under Rule 16b-3.  The restricted stock units become payable in Common Stock on the vesting date of 02/10/2023.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James F. Stern, Attorney-in-Fact for Wallace E. Goodwain</signatureName>
        <signatureDate>2022-02-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
