Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Numerator:
Net income (loss)		$ 466,389	$ 485,845	$ 377,715	$ 981,343
Amounts attributable to noncontrolling interests		(167,568)	(16,891)	65,223	(63,861)
Net income available to Arch		298,821	468,954	442,938	917,482
Preferred dividends		(10,403)	(10,403)	(20,806)	(20,806)
Net income available to Arch common shareholders		$ 288,418	$ 458,551	$ 422,132	$ 896,676
Denominator:
Weighted average common shares outstanding — basic		402,503,687	401,482,784	403,197,924	400,837,181
Effect of dilutive common share equivalents:
Nonvested restricted shares		1,597,701	1,937,626	1,829,239	1,720,417
Stock options	[1]	4,018,293	7,479,073	5,978,428	7,197,652
Weighted average common shares and common share equivalents outstanding — diluted		408,119,681	410,899,483	411,005,591	409,755,250
Earnings per common share:
Basic (per share)		$ 0.72	$ 1.14	$ 1.05	$ 2.24
Diluted (per share)		$ 0.71	$ 1.12	$ 1.03	$ 2.19
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		6,982,107	2,016,830	2,038,758	2,560,755

[1] 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 the 2020 second quarter and 2019 second quarter, the number of stock options excluded were 6,982,107 and 2,016,830, respectively. For the six months ended June 30, 2020 and 2019 period, the number of stock options excluded were 2,038,758 and 2,560,755, respectively.