<SEC-DOCUMENT>0000091142-20-000058.txt : 20201103
<SEC-HEADER>0000091142-20-000058.hdr.sgml : 20201103
<ACCEPTANCE-DATETIME>20201103141244
ACCESSION NUMBER:		0000091142-20-000058
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20201102
FILED AS OF DATE:		20201103
DATE AS OF CHANGE:		20201103

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			JONES PAUL W
		CENTRAL INDEX KEY:			0001111599

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-00475
		FILM NUMBER:		201283025

	MAIL ADDRESS:	
		STREET 1:		900 COMMERCE DRIVE, SUITE 302
		CITY:			OAK BROOK
		STATE:			IL
		ZIP:			60523

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>2020-11-02</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001111599</rptOwnerCik>
            <rptOwnerName>JONES PAUL W</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>2020-11-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>52.3937</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>173216</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>52.4956</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>163216</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>12069</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>52.6802</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>151147</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price in Column 4 is a weighted average price.  The prices actually received ranged from $52.30 to $52.61.  The reporting person has provided to the issuer, and will provide to any security holder of the issuer, or the SEC staff, upon request, information regarding the number of shares sold at each price within the range for all transactions reported on this Form 4 utilizing an average weighted price.</footnote>
        <footnote id="F2">The price in Column 4 is a weighted average price.  The prices actually received ranged from $52.41 to $52.645.  The reporting person has provided to the issuer, and will provide to any security holder of e issuer, or the SEC staff, upon request, information regarding the number of shares sold at each price within the range for all transactions reported on this Form 4 utilizing an average weighted price.</footnote>
        <footnote id="F3">The price in Column 4 is a weighted average price.  The prices actually received ranged from $52.61 to $52.79.  The reporting person has provided to the issuer, and will provide to any security holder of the issuer, or the SEC staff, upon request, information regarding the number of shares sold at each price within the range for all transactions reported on this Form 4 utilizing an average weighted price.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James F. Stern, Attorney-in-Fact for Paul W. Jones</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
