Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Numerator:
Net income (loss)		$ 403,945	$ 718,664	$ 601,377	$ 1,194,372
Amounts attributable to noncontrolling interests		399	(43,178)	(1,233)	(80,730)
Net income available to Arch		404,344	675,486	600,144	1,113,642
Preferred dividends		(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders		$ 394,160	$ 663,820	$ 579,776	$ 1,091,573
Denominator:
Weighted average common shares outstanding — basic		369,241,193	397,743,402	371,728,683	399,267,183
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,121,678	1,990,729	2,238,267	1,932,929
Stock options	[1]	6,590,117	6,751,863	6,938,562	6,487,568
Weighted average common shares and common share equivalents outstanding — diluted		377,952,988	406,485,994	380,905,512	407,687,680
Earnings per common share:
Basic (per share)		$ 1.07	$ 1.67	$ 1.56	$ 2.73
Diluted (per share)		$ 1.04	$ 1.63	$ 1.52	$ 2.68
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		773,163	1,974,849	778,724	2,395,749

[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 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.