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Earnings Per Common Share (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 9 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2021
Sep. 30, 2020
Numerator:        
Net income (loss) $ 421,415 $ 488,682 $ 1,615,787 $ 866,397
Amounts attributable to noncontrolling interests (1,473) (69,643) (82,203) (4,420)
Net income available to Arch 419,942 419,039 1,533,584 861,977
Preferred dividends (16,090) (10,403) (38,159) (31,209)
Loss on redemption of preferred shares (15,101) 0 (15,101) 0
Net income (loss) available to Arch common shareholders $ 388,751 $ 408,636 $ 1,480,324 $ 830,768
Denominator:        
Weighted average common shares outstanding — basic 389,274,220 402,850,485 395,899,591 403,081,266
Effect of dilutive common share equivalents:        
Nonvested restricted shares 2,131,915 1,580,791 1,877,930 1,690,447
Stock options [1] 6,497,212 4,763,381 6,482,964 5,543,184
Weighted average common shares and common share equivalents outstanding — diluted 397,903,347 409,194,657 404,260,485 410,314,897
Earnings per common share:        
Basic (per share) $ 1.00 $ 1.01 $ 3.74 $ 2.06
Diluted (per share) $ 0.98 $ 1.00 $ 3.66 $ 2.02
Stock options        
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]        
Antidilutive securities excluded from computation of earnings per common share (shares) 1,948,006 4,713,241 2,397,507 2,361,413
[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 2021 third quarter and 2020 third quarter, the number of stock options excluded were 1,948,006 and 4,713,241, respectively. For the nine months ended September 30, 2021 and 2020 period, the number of stock options excluded were 2,397,507 and 2,361,413, respectively.