| Document and Entity Information | Jul. 30, 2020 |
| Cover [Abstract] | |
| Entity Registrant Name | SMITH A O CORP |
| Amendment Flag | false |
| Entity Central Index Key | 0000091142 |
| Document Type | 8-K |
| Document Period End Date | Jul. 30, 2020 |
| Entity Incorporation State Country Code | DE |
| Entity File Number | 1-475 |
| Entity Tax Identification Number | 39-0619790 |
| Entity Address, Address Line One | 11270 West Park Place |
| Entity Address, City or Town | Milwaukee |
| Entity Address, State or Province | WI |
| Entity Address, Postal Zip Code | 53224 |
| City Area Code | (414) |
| Local Phone Number | 359-4000 |
| Written Communications | false |
| Soliciting Material | false |
| Pre Commencement Tender Offer | false |
| Pre Commencement Issuer Tender Offer | false |
| Security 12b Title | Common Stock (par value $1.00 per share) |
| Trading Symbol | AOS |
| Security Exchange Name | NYSE |
| Entity Emerging Growth Company | false |
