| **Debt (Details) $ in Millions**                                      | Dec. 31, 2021 USD ($) covenant |
|-----------------------------------------------------------------------|--------------------------------|
| **Debt Disclosure [Abstract]**                                        |                           |
| Multi-currency revolving credit agreement, maximum borrowing capacity | $ 500                          |
| Accordion feature, higher borrowing capacity option                   | $ 850                          |
| Number of required financial covenants | covenant                     | 2                              |

| X                                                                                                                                                                                                                                                                                                                                  |
|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Line of Credit Facility, Accordion Feature, Higher Borrowing Capacity Option
+ References
No definition available.
+ Details**Name:**aos_LineOfCreditFacilityAccordionFeatureHigherBorrowingCapacityOption**Namespace Prefix:**aos_**Data Type:**xbrli:monetaryItemType**Balance Type:**credit**Period Type:**instant |
| X                                                                                                                                                                                                                                                                                               |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Line of Credit Facility, Financial Covenant Required, Number
+ References
No definition available.
+ Details**Name:**aos_LineOfCreditFacilityFinancialCovenantRequiredNumber**Namespace Prefix:**aos_**Data Type:**xbrli:integerItemType**Balance Type:**na**Period Type:**instant |
| X                                                                                                                                                                                                |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - References
No definition available.
+ Details**Name:**us-gaap_DebtDisclosureAbstract**Namespace Prefix:**us-gaap_**Data Type:**xbrli:stringItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.
+ References
Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 210 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02.19(b),22(b)) -URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682
+ Details**Name:**us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity**Namespace Prefix:**us-gaap_**Data Type:**xbrli:monetaryItemType**Balance Type:**credit**Period Type:**instant |