Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Numerator:
Net income (loss)		$ 18,258	$ 421,415	$ 619,635	$ 1,615,787
Amounts attributable to noncontrolling interests		(1,157)	(1,473)	(2,390)	(82,203)
Net income available to Arch		17,101	419,942	617,245	1,533,584
Preferred dividends		(10,184)	(16,090)	(30,552)	(38,159)
Loss on redemption of preferred shares		0	(15,101)	0	(15,101)
Net income (loss) available to Arch common shareholders		$ 6,917	$ 388,751	$ 586,693	$ 1,480,324
Denominator:
Weighted average common shares outstanding — basic		365,190,527	389,274,220	369,525,348	395,899,591
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,351,039	2,131,915	2,171,158	1,877,930
Stock options	[1]	6,185,711	6,497,212	6,676,674	6,482,964
Weighted average common shares and common share equivalents outstanding — diluted		373,727,277	397,903,347	378,373,180	404,260,485
Earnings per common share:
Basic (per share)		$ 0.02	$ 1.00	$ 1.59	$ 3.74
Diluted (per share)		$ 0.02	$ 0.98	$ 1.55	$ 3.66
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		774,481	1,948,006	785,682	2,397,507

[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 third quarter and 2021 third quarter, the number of stock options excluded were 774,481 and 1,948,006, respectively. For the nine months ended September 30, 2022 and 2021, the number of stock options excluded were 785,682 and 2,397,507, respectively.