| **Stock Based Compensation - Nonvested Stock Options (Details)**           | 12 Months Ended |
|----------------------------------------------------------------------------|-----------------|
||
| **Number of Options**                                                      |            |
| Nonvested options at beginning of year (in shares) | shares                | 806,054         |
| Vested (in shares) | shares                                                | (477,245)       |
| Forfeited (in shares) | shares                                             | (6,005)         |
| Nonvested options at end of year (in shares) | shares                      | 322,804         |
| **Weighted Avg. Per Share Exercise Price**                                 |            |
| Nonvested options at beginning of year (in dollars per share) | $ / shares | $ 60.26         |
| Vested (in dollars per share) | $ / shares                                 | 54.05           |
| Forfeited (in dollars per share) | $ / shares                              | 66.24           |
| Nonvested options at end of year (in dollars per share) | $ / shares       | $ 69.33         |

| X                                                                                                                                                                                                                                                                                                                                                                                                                                  |
|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Share-based Compensation Arrangement by Share-based Payment Award, Options, Nonvested, Weighted Average Grant Date Fair Value
+ References
No definition available.
+ Details**Name:**aos_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValueRollForward**Namespace Prefix:**aos_**Data Type:**xbrli:stringItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                       |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Number of non-vested options outstanding.
+ References
No definition available.
+ Details**Name:**us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares**Namespace Prefix:**us-gaap_**Data Type:**xbrli:sharesItemType**Balance Type:**na**Period Type:**instant |
| X                                                                                                                                                                                                                                                                                                                                                                                                |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.
+ References
No definition available.
+ Details**Name:**us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfSharesRollForward**Namespace Prefix:**us-gaap_**Data Type:**xbrli:stringItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                      |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Number of non-vested options forfeited.
+ References
No definition available.
+ Details**Name:**us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedOptionsForfeitedNumberOfShares**Namespace Prefix:**us-gaap_**Data Type:**xbrli:sharesItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                               |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Weighted average grant-date fair value of non-vested options forfeited.
+ References
No definition available.
+ Details**Name:**us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedOptionsForfeitedWeightedAverageGrantDateFairValue**Namespace Prefix:**us-gaap_**Data Type:**dtr-types:perShareItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Weighted average grant-date fair value of non-vested options outstanding.
+ References
No definition available.
+ Details**Name:**us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue**Namespace Prefix:**us-gaap_**Data Type:**dtr-types:perShareItemType**Balance Type:**na**Period Type:**instant |
| X                                                                                                                                                                                                                                                                                                     |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Number of options vested.
+ References
No definition available.
+ Details**Name:**us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares**Namespace Prefix:**us-gaap_**Data Type:**xbrli:sharesItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                              |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Weighted average grant-date fair value of options vested.
+ References
No definition available.
+ Details**Name:**us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedWeightedAverageGrantDateFairValue**Namespace Prefix:**us-gaap_**Data Type:**dtr-types:perShareItemType**Balance Type:**na**Period Type:**duration |