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Earnings Per Common Share (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 9 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2020
Sep. 30, 2019
Numerator:        
Net income (loss) $ 488,682 $ 399,189 $ 866,397 $ 1,380,532
Amounts attributable to noncontrolling interests (69,643) (6,736) (4,420) (70,597)
Net income available to Arch 419,039 392,453 861,977 1,309,935
Preferred dividends (10,403) (10,403) (31,209) (31,209)
Net income (loss) available to Arch common shareholders $ 408,636 $ 382,050 $ 830,768 $ 1,278,726
Denominator:        
Weighted average common shares outstanding — basic 402,850,485 402,564,121 403,081,266 401,419,153
Effect of dilutive common share equivalents:        
Nonvested restricted shares 1,580,791 1,895,972 1,690,447 1,637,015
Stock options [1] 4,763,381 8,720,108 5,543,184 7,751,234
Weighted average common shares and common share equivalents outstanding — diluted 409,194,657 413,180,201 410,314,897 410,807,402
Earnings per common share:        
Basic (per share) $ 1.01 $ 0.95 $ 2.06 $ 3.19
Diluted (per share) $ 1.00 $ 0.92 $ 2.02 $ 3.11
Stock options        
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]        
Antidilutive securities excluded from computation of earnings per common share (shares) 4,713,241 37,394 2,361,413 2,198,115
[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 2020 third quarter and 2019 third quarter, the number of stock options excluded were 4,713,241 and 37,394, respectively. For the nine months ended September 30, 2020 and 2019 period, the number of stock options excluded were 2,361,413 and 2,198,115, respectively.