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Share-Based Compensation - Additional information (Details) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period 3 years    
Stock Options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period 3 years    
Life of award 10 years    
Share based compensation expense $ 12.5us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 10.6us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 8.5us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
Tax benefit 2.1us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
2.0us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
1.8us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
Unrecognized compensation cost related to unvested awards 14.8us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
   
Expected period for recognition (years) 1 year 9 months 18 days    
Weighted average grant date fair value $ 14.77us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 12.96us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 10.61us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
Aggregate intrinsic value of options exercised 58.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
21.7us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
64.0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
Aggregate intrinsic value of options outstanding 191.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
   
Aggregate intrinsic value of options exercisable 167.8us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
   
Options outstanding, weighted average remaining contractual term (in years) 5 years 8 months 12 days    
Options exercisable, weighted average remaining contractual term (in years) 4 years 7 months 6 days    
Proceeds from stock options exercised 11.0us-gaap_ProceedsFromStockOptionsExercised
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
   
Tax benefit from stock options exercised 8.9us-gaap_DeferredTaxExpenseFromStockOptionsExercised
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
   
Restricted Common Shares And Restricted Units      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period 3 years    
Share based compensation expense 30.0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
27.4us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
24.6us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
Tax benefit 8.4us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
7.8us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
6.3us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
Granted (in shares) 767,469us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
590,118us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
1,819,657us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
Granted, weighted average grant date fair value $ 56.97us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
$ 53.21us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
$ 40.75us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
Aggregate fair value of awards that vested in the period 38.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
41.0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
33.2us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= acgl_RestrictedCommonSharesAndRestrictedUnitsMember
Restricted Common Shares      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Unrecognized compensation cost related to unvested awards 48.5us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Expected period for recognition (years) 1 year 8 months 12 days    
Granted (in shares) 660,043us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Granted, weighted average grant date fair value $ 56.94us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Restricted Unit Awards      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Unrecognized compensation cost related to unvested awards 8.1us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
   
Expected period for recognition (years) 1 year 9 months 18 days    
Granted (in shares) 107,426us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
   
Granted, weighted average grant date fair value $ 57.18us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
   
Aggregate intrinsic value of awards outstanding 26.4us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
   
Aggregate intrinsic value of awards exercisable $ 8.4acgl_ShareBasedPaymentAwardOtherThanOptionsExercisableAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember