Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Numerator:
Net income		$ 1,482,423	$ 2,239,462	$ 1,465,711
Net (income) loss attributable to noncontrolling interests		(5,490)	(82,613)	(60,190)
Net income available to Arch		1,476,933	2,156,849	1,405,521
Preferred share dividends		(40,736)	(48,343)	(41,612)
Loss on redemption of preferred shares		0	(15,101)	0
Net income available to Arch common shareholders		$ 1,436,197	$ 2,093,405	$ 1,363,909
Denominator:
Weighted average common shares outstanding		368,612,197	391,748,715	403,062,179
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,103,036	1,996,524	1,682,309
Stock options	[1]	6,894,534	6,600,697	5,514,967
Weighted average common shares and common share equivalents outstanding — diluted		377,609,767	400,345,936	410,259,455
Earnings per common share:
Basic (per share)		$ 3.90	$ 5.34	$ 3.38
Diluted (per share)		$ 3.80	$ 5.23	$ 3.32
Stock Options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		798,053	2,398,608	2,249,821

[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 2022, 2021 and 2020, the number of stock options excluded were 798,053, 2,398,608 and 2,249,821, respectively.