| **Derivative Instruments - Narrative (Details) - USD ($) $ in Millions**                                             | 3 Months Ended |        |
|----------------------------------------------------------------------------------------------------------------------|----------------|--------|
||
| **Trading Activity, Gains and Losses, Net [Line Items]**                                                             |           |   |   |
| After-tax gains (losses) associated with currency translation adjustment in other comprehensive income               | $ (4.8)        | $ 2.5  |   |
| Commodity Futures Contracts                                                                                          |           |   |   |
| **Trading Activity, Gains and Losses, Net [Line Items]**                                                             |           |   |   |
| Reclassification period for effective portion of contract, in years                                                  | 1 year         |   |   |
| Designated as Hedging Instrument | Foreign Exchange Contract | Other Current Assets                                  |           |   |   |
| **Trading Activity, Gains and Losses, Net [Line Items]**                                                             |           |   |   |
| Fair value of derivative instruments, assets                                                                         | $ 2.3          |   | $ 0.9 |
| Not Designated as Hedging Instrument | Foreign Exchange Contract | Accrued Liabilities                               |           |   |   |
| **Trading Activity, Gains and Losses, Net [Line Items]**                                                             |           |   |   |
| Fair value of derivative instruments, liability                                                                      | 0.3            |   | 0.8 |
| Net Investment Hedges | Designated as Hedging Instrument | Foreign currency forward contracts | Other Current Assets |           |   |   |
| **Trading Activity, Gains and Losses, Net [Line Items]**                                                             |           |   |   |
| Fair value of derivative instruments, assets                                                                         | 1.1            |   |   |
| Net Investment Hedges | Designated as Hedging Instrument | Foreign currency forward contracts | Accrued Liabilities  |           |   |   |
| **Trading Activity, Gains and Losses, Net [Line Items]**                                                             |           |   |   |
| Fair value of derivative instruments, liability                                                                      |           |   | $ 4.2 |
| Net Investment Hedges | Non-U.S. | Designated as Hedging Instrument | Foreign currency forward contracts             |           |   |   |
| **Trading Activity, Gains and Losses, Net [Line Items]**                                                             |           |   |   |
| After-tax gains (losses) associated with currency translation adjustment in other comprehensive income               | 4.0            | $ 0.5  |   |
| Contractual amounts                                                                                                  | $ 204.0        |   |   |

| X                                                                                                                                                                                                                                                                                              |
|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Reclassification Period For Effective Portion Of Contract
+ References
No definition available.
+ Details**Name:**aos_ReclassificationPeriodForEffectivePortionOfContract**Namespace Prefix:**aos_**Data Type:**xbrli:durationItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |
|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Fair value, before effects of master netting arrangements, of a financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes assets elected not to be offset. Excludes assets not subject to a master netting arrangement.
+ References
Reference 1: http://www.xbrl.org/2003/role/exampleRef -Topic 210 -SubTopic 20 -Name Accounting Standards Codification -Section 55 -Paragraph 22 -Publisher FASB -URI https://asc.fasb.org//1943274/2147483444/210-20-55-22Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 210 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org//1943274/2147483466/210-20-50-3Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 20 -Name Accounting Standards Codification -Section 55 -Paragraph 7 -Publisher FASB -URI https://asc.fasb.org//1943274/2147483444/210-20-55-7Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 815 -SubTopic 10 -Section 50 -Paragraph 4B -Subparagraph (a),(c) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480434/815-10-50-4BReference 5: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 50 -Paragraph 4D -Subparagraph (c)(2) -SubTopic 20 -Topic 860 -Publisher FASB -URI https://asc.fasb.org//1943274/2147481326/860-20-50-4D
+ Details**Name:**us-gaap_DerivativeFairValueOfDerivativeAsset**Namespace Prefix:**us-gaap_**Data Type:**xbrli:monetaryItemType**Balance Type:**debit**Period Type:**instant |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Fair value, before effects of master netting arrangements, of a financial liability or contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes liabilities elected not to be offset. Excludes liabilities not subject to a master netting arrangement.
+ References
Reference 1: http://www.xbrl.org/2003/role/exampleRef -Topic 210 -SubTopic 20 -Name Accounting Standards Codification -Section 55 -Paragraph 22 -Publisher FASB -URI https://asc.fasb.org//1943274/2147483444/210-20-55-22Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 210 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org//1943274/2147483466/210-20-50-3Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 20 -Name Accounting Standards Codification -Section 55 -Paragraph 7 -Publisher FASB -URI https://asc.fasb.org//1943274/2147483444/210-20-55-7Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 815 -SubTopic 10 -Section 50 -Paragraph 4B -Subparagraph (a),(c) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480434/815-10-50-4BReference 5: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 50 -Paragraph 4D -Subparagraph (c)(2) -SubTopic 20 -Topic 860 -Publisher FASB -URI https://asc.fasb.org//1943274/2147481326/860-20-50-4D
+ Details**Name:**us-gaap_DerivativeFairValueOfDerivativeLiability**Namespace Prefix:**us-gaap_**Data Type:**xbrli:monetaryItemType**Balance Type:**credit**Period Type:**instant |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Nominal or face amount used to calculate payment on derivative.
+ References
Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 815 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 1B -Publisher FASB -URI https://asc.fasb.org//1943274/2147480434/815-10-50-1BReference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 815 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 1A -Subparagraph (d) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480434/815-10-50-1A
+ Details**Name:**us-gaap_DerivativeNotionalAmount**Namespace Prefix:**us-gaap_**Data Type:**xbrli:monetaryItemType**Balance Type:**na**Period Type:**instant |
| X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |
|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Amount after tax and reclassification adjustments of gain (loss) on foreign currency translation adjustments, foreign currency transactions designated and effective as economic hedges of a net investment in a foreign entity and intra-entity foreign currency transactions that are of a long-term-investment nature.
+ References
Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 45 -Paragraph 10A -Subparagraph (a) -SubTopic 10 -Topic 220 -Publisher FASB -URI https://asc.fasb.org//1943274/2147482790/220-10-45-10A
+ Details**Name:**us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax**Namespace Prefix:**us-gaap_**Data Type:**xbrli:monetaryItemType**Balance Type:**credit**Period Type:**duration |
| X                                                                                                                                                                                                                                                                                                                                                                                                                              |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.
+ References
No definition available.
+ Details**Name:**us-gaap_TradingActivityGainsAndLossesLineItems**Namespace Prefix:**us-gaap_**Data Type:**xbrli:stringItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                             |
|---------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_TradingActivityByTypeAxis=aos_CommodityFuturesContractsMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                                                  |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_HedgingDesignationAxis=us-gaap_DesignatedAsHedgingInstrumentMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                                                  |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_DerivativeInstrumentRiskAxis=us-gaap_ForeignExchangeContractMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                                         |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_BalanceSheetLocationAxis=us-gaap_OtherCurrentAssetsMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                                  |
|----------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_HedgingDesignationAxis=us-gaap_NondesignatedMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                                         |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_BalanceSheetLocationAxis=us-gaap_AccruedLiabilitiesMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                                                                         |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis=us-gaap_NetInvestmentHedgingMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                                                 |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**us-gaap_DerivativeInstrumentRiskAxis=us-gaap_ForeignExchangeForwardMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |
| X                                                                                                                                         |
|-------------------------------------------------------------------------------------------------------------------------------------------|
| - Details**Name:**srt_StatementGeographicalAxis=us-gaap_NonUsMember**Namespace Prefix:****Data Type:**na**Balance Type:****Period Type:** |