<SEC-DOCUMENT>0000091142-22-000085.txt : 20220901
<SEC-HEADER>0000091142-22-000085.hdr.sgml : 20220901
<ACCEPTANCE-DATETIME>20220901142749
ACCESSION NUMBER:		0000091142-22-000085
CONFORMED SUBMISSION TYPE:	3
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20220901
FILED AS OF DATE:		20220901
DATE AS OF CHANGE:		20220901

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Kulkarni Parag
		CENTRAL INDEX KEY:			0001944750

	FILING VALUES:
		FORM TYPE:		3
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-00475
		FILM NUMBER:		221220591

	MAIL ADDRESS:	
		STREET 1:		A. O. SMITH INDIA WATER PRODUCTS PRIVATE
		STREET 2:		#300, PHASE II, KIADB INDUSTRIAL AREA
		CITY:			KARNATAKA
		STATE:			K7
		ZIP:			562112

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>3
<SEQUENCE>1
<FILENAME>wf-form3_166205685520178.xml
<DESCRIPTION>FORM 3
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-09-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001944750</rptOwnerCik>
            <rptOwnerName>Kulkarni Parag</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>A. O. SMITH INDIA WATER PRODUCTS PRIVATE</rptOwnerStreet1>
            <rptOwnerStreet2>#300, PHASE II, KIADB INDUSTRIAL AREA</rptOwnerStreet2>
            <rptOwnerCity>KARNATAKA</rptOwnerCity>
            <rptOwnerState>K7</rptOwnerState>
            <rptOwnerZipCode>562112</rptOwnerZipCode>
            <rptOwnerStateDescription>INDIA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP - Int'l; President India</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1770.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Employee Stock Options (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>33.235</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-04-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1720.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted stock units were granted under the A. O. Smith Combined Incentive Compensation Plan, a transaction exempt under Rule 16b-3:  780 Restricted stock units were granted on 02/10/2020 and they become payable in cash on the vesting date of 02/10/2023.  545 Restricted stock units were granted on 02/08/2021 and they become payable in cash on the vesting date of 02/08/2024.  445 Restricted stock units were granted on 02/07/2022 and they become payable in cash on the vesting date of 02/07/2025.</footnote>
        <footnote id="F2">Each restricted stock unit is the economic equivalent of one share of A. O. Smith Corporation Common Stock.</footnote>
        <footnote id="F3">Employee stock options were granted on 04/27/2015, under the A. O. Smith Combined Incentive Compensation Plan, a transaction exempt under rule 16b-3.  The option became exercisable in three annual installments of 1/3 of the award starting on 04/27/2016.  The stock options are payable in cash when exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James F. Stern, Attorney-in-Factor for Parag Kulkarni</signatureName>
        <signatureDate>2022-09-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
