| **Stock Based Compensation - Schedule of Performance Stock Unit Activity (Details) - Performance Shares - $ / shares** | 3 Months Ended |
|------------------------------------------------------------------------------------------------------------------------|----------------|
||
| **Number of Units**                                                                                                    |           |   |
| Beginning balance (in shares)                                                                                          | 34,758         |   |
| Granted (in shares)                                                                                                    | 28,390         | 24,580 |
| Performance adjustments (in shares)                                                                                    | 1,550          |   |
| Ending balance (in shares)                                                                                             | 64,698         |   |
| **Weighted-Average Grant Date Value**                                                                                  |           |   |
| Beginning balance (in USD per share)                                                                                   | $ 67.14        |   |
| Granted (in USD per share)                                                                                             | 82.04          |   |
| Performance adjustments (in USD per share)                                                                             | 67.14          |   |
| Ending balance (in USD per share)                                                                                      | $ 73.68        |   |

| X                                                                                                                                                                                                                                                                                                                                                                                                                                 |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Performance Adjustments
+ References
No definition available.
+ Details**Name:**aos_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPerformanceAdjustments**Namespace Prefix:**aos_**Data Type:**xbrli:sharesItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Performance Adjustments, Weighted Average Grant Date Fair Value
+ References
No definition available.
+ Details**Name:**aos_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPerformanceAdjustmentsWeightedAverageGrantDateFairValue**Namespace Prefix:**aos_**Data Type:**dtr-types1:perShareItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Share-based Compensation Arrangement by Share-based Payment Award, Non-Option Equity Instruments, Nonvested, Weighted Average Exercise Price
+ References
No definition available.
+ Details**Name:**aos_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsNonvestedWeightedAverageExercisePriceRollForward**Namespace Prefix:**aos_**Data Type:**xbrli:stringItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).
+ References
Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2)(iii)(01) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2
+ Details**Name:**us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod**Namespace Prefix:**us-gaap_**Data Type:**xbrli:sharesItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).
+ References
Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2)(iii)(01) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2
+ Details**Name:**us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue**Namespace Prefix:**us-gaap_**Data Type:**dtr-types:perShareItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.
+ References
Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2)(i) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2)(ii) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2
+ Details**Name:**us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber**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_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward**Namespace Prefix:**us-gaap_**Data Type:**xbrli:stringItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.
+ References
Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2)(i) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2)(ii) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2
+ Details**Name:**us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue**Namespace Prefix:**us-gaap_**Data Type:**dtr-types:perShareItemType**Balance Type:**na**Period Type:**instant |
| X                                                                                                                                             |
|-----------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_AwardTypeAxis=us-gaap_PerformanceSharesMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |