| | | | | | | | | | | | | | | | | | | | | |
<?xml version="1.0" encoding="windows-1252"?> |
<ownershipDocument> |
| <schemaVersion> X0306 </schemaVersion> |
| <documentType> 4/A </documentType> |
| <periodOfReport> 2022-09-01 </periodOfReport> |
| <dateOfOriginalSubmission> 2022-09-02 </dateOfOriginalSubmission> |
| <notSubjectToSection16> 0 </notSubjectToSection16> |
| <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> |
| | <derivativeTransaction> |
| | | <securityTitle> |
| <value> Restricted Stock Units </value> |
| </securityTitle> |
| | | <conversionOrExercisePrice> |
| <value> 56.07 </value> |
| <footnoteId id="F1"/> |
| </conversionOrExercisePrice> |
| | | <transactionDate> |
| <value> 2022-09-01 </value> |
| </transactionDate> |
| | | <transactionCoding> |
| <transactionFormType> 4 </transactionFormType> |
| <transactionCode> A </transactionCode> |
| <equitySwapInvolved> 0 </equitySwapInvolved> |
| </transactionCoding> |
| | | <transactionAmounts> |
| <transactionShares> |
| <value> 2140 </value> |
| </transactionShares> |
| <transactionPricePerShare> |
| <value> 0 </value> |
| </transactionPricePerShare> |
| <transactionAcquiredDisposedCode> |
| <value> A </value> |
| </transactionAcquiredDisposedCode> |
| </transactionAmounts> |
| | | <exerciseDate> |
| <footnoteId id="F2"/> |
| </exerciseDate> |
| | | <expirationDate> |
| <footnoteId id="F2"/> |
| </expirationDate> |
| | | <underlyingSecurity> |
| <underlyingSecurityTitle> |
| <value> Common Stock </value> |
| </underlyingSecurityTitle> |
| <underlyingSecurityShares> |
| <value> 2140.0 </value> |
| </underlyingSecurityShares> |
| </underlyingSecurity> |
| | | <postTransactionAmounts> |
| <sharesOwnedFollowingTransaction> |
| <value> 3910 </value> |
| </sharesOwnedFollowingTransaction> |
| </postTransactionAmounts> |
| | | <ownershipNature> |
| <directOrIndirectOwnership> |
| <value> D </value> |
| </directOrIndirectOwnership> |
| </ownershipNature> |
| | | </derivativeTransaction> |
| | </derivativeTable> |
| <footnotes> |
| | <footnote id="F1"> Each restricted stock unit is the economic equivalent of one share of A. O. Smith Corporation Common Stock. </footnote> |
| | <footnote id="F2"> The restricted stock units were granted on 09/01/2022 under the A. O. Smith Combined Incentive Compensation Plan, a transaction exempt under Rule 16b-3. The restricted stock units become payable in cash on the vesting date of 09/01/2025. </footnote> |
| | </footnotes> |
| <remarks></remarks> |
| <ownerSignature> |
| | <signatureName> James F. Stern, Attorney-in-Factor for Parag Kulkarni </signatureName> |
| | <signatureDate> 2022-09-20 </signatureDate> |
| | </ownerSignature> |
| </ownershipDocument> |