Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended
		Mar. 31, 2022	Mar. 31, 2021
Numerator:
Net income (loss)		$ 197,432	$ 475,708
Amounts attributable to noncontrolling interests		(1,632)	(37,552)
Net income available to Arch		195,800	438,156
Preferred dividends		(10,184)	(10,403)
Net income (loss) available to Arch common shareholders		$ 185,616	$ 427,753
Denominator:
Weighted average common shares outstanding — basic		374,243,812	400,807,895
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,659,922	2,230,794
Stock options	[1]	7,290,629	6,184,564
Weighted average common shares and common share equivalents outstanding — diluted		384,194,363	409,223,253
Earnings per common share:
Basic (per share)		$ 0.50	$ 1.07
Diluted (per share)		$ 0.48	$ 1.05
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		769,026	2,400,082

[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 2022 first quarter and 2021 first quarter, the number of stock options excluded were 769,026 and 2,400,082, respectively.