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Earnings Per Common Share (Details) - USD ($)
$ / shares in Units, $ in Thousands
 12 Months Ended
Dec. 31, 2021
Dec. 31, 2020
Dec. 31, 2019
Numerator:      
Net income $ 2,239,462 $ 1,465,711 $ 1,693,300
Net (income) loss attributable to noncontrolling interests (82,613) (60,190) (56,981)
Net income available to Arch 2,156,849 1,405,521 1,636,319
Preferred share dividends (48,343) (41,612) (41,612)
Loss on redemption of preferred shares (15,101) 0 0
Net income available to Arch common shareholders $ 2,093,405 $ 1,363,909 $ 1,594,707
Denominator:      
Weighted average common shares outstanding 391,748,715 403,062,179 401,802,815
Effect of dilutive common share equivalents:      
Nonvested restricted shares 1,996,524 1,682,309 1,673,770
Stock options [1] 6,600,697 5,514,967 8,132,893
Weighted average common shares and common share equivalents outstanding — diluted 400,345,936 410,259,455 411,609,478
Earnings per common share:      
Basic (per share) $ 5.34 $ 3.38 $ 3.97
Diluted (per share) $ 5.23 $ 3.32 $ 3.87
Stock Options      
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]      
Antidilutive securities excluded from computation of earnings per common share (shares) 2,398,608 2,249,821 1,302,017
[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 2021, 2020 and 2019, the number of stock options excluded were 2,398,608, 2,249,821 and 1,302,017, respectively.