Earnings Per Common Share (Details) (USD $) In Thousands, except Share data, unless otherwise specified	3 Months Ended								12 Months Ended
	Dec. 31, 2014	Sep. 30, 2014	Jun. 30, 2014	Mar. 31, 2014	Dec. 31, 2013	Sep. 30, 2013	Jun. 30, 2013	Mar. 31, 2013	Dec. 31, 2014		Dec. 31, 2013		Dec. 31, 2012
Numerator:
Net income	$ 207,134	$ 223,264	$ 211,717	$ 179,145	$ 161,490	$ 114,825	$ 176,940	$ 256,476	$ 821,260		$ 709,731		$ 593,397
Amounts attributable to noncontrolling interests									13,095	[1]	0	[1]	0	[1]
Net income available to Arch									834,355		709,731		593,397
Preferred dividends	(5,485)	(5,484)	(5,485)	(5,484)	(5,485)	(5,484)	(5,485)	(5,484)	(21,938)		(21,938)		(25,079)
Loss on repurchase of preferred shares									0		0		(10,612)
Net income available to common shareholders	$ 209,679	$ 223,191	$ 202,531	$ 177,016	$ 156,005	$ 109,341	$ 171,455	$ 250,992	$ 812,417		$ 687,793		$ 557,706
Denominator:
Weighted average common shares outstanding — basic									130,817,610		131,355,392		134,446,158
Effect of dilutive common share equivalents:
Nonvested restricted shares									1,128,540		1,090,100		857,174
Stock options									2,976,172	[2]	3,331,691	[2]	2,955,515	[2]
Weighted average common shares and common share equivalents outstanding — diluted									134,922,322		135,777,183		138,258,847
Earnings per common share:
Basic (per share)	$ 1.65	$ 1.69	$ 1.53	$ 1.34	$ 1.19	$ 0.83	$ 1.31	$ 1.92	$ 6.21		$ 5.24		$ 4.15
Diluted (per share)	$ 1.60	$ 1.64	$ 1.48	$ 1.30	$ 1.14	$ 0.80	$ 1.26	$ 1.85	$ 6.02		$ 5.07		$ 4.03
Stock Options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)									1,435,955		892,439		839,414

[1] See Note 4.

[2] Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2014, 2013 and 2012, the number of stock options excluded were 1,435,955, 892,439 and 839,414, respectively.