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Accounting for Income Taxes - Additional Information (Details) (USD $)
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Income Taxes [Line Items]    
Provision for income taxes $ 11,295,000us-gaap_IncomeTaxExpenseBenefit $ 9,961,000us-gaap_IncomeTaxExpenseBenefit
Effective income tax rate, continuing operations 23.80%us-gaap_EffectiveIncomeTaxRateContinuingOperations 23.50%us-gaap_EffectiveIncomeTaxRateContinuingOperations
Statutory rate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate  
Valuation allowance, deferred tax asset 32,700,000us-gaap_DeferredTaxAssetsValuationAllowance  
Unrecognized tax benefits 34,400,000us-gaap_UnrecognizedTaxBenefits  
Tax holiday effect on diluted earnings per share $ 0.10algn_EffectiveIncomeTaxRateReconciliationTaxHolidayEffectonDilutedEarningsPerShare $ 0.09algn_EffectiveIncomeTaxRateReconciliationTaxHolidayEffectonDilutedEarningsPerShare
Foreign Tax Authority [Member]    
Income Taxes [Line Items]    
Foreign income tax rate 30.00%algn_EffectiveIncomeTaxReconciliationatForeignIncomeTaxRate
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember
 
Tax Holiday effect $ 8,200,000us-gaap_IncomeTaxReconciliationTaxHolidays
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember
$ 7,600,000us-gaap_IncomeTaxReconciliationTaxHolidays
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember