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Earnings Per Common Share (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended
Mar. 31, 2021
Mar. 31, 2020
Numerator:    
Net income (loss) $ 475,708 $ (88,674)
Amounts attributable to noncontrolling interests (37,552) 232,791
Net income available to Arch 438,156 144,117
Preferred dividends (10,403) (10,403)
Net income (loss) available to Arch common shareholders $ 427,753 $ 133,714
Denominator:    
Weighted average common shares outstanding — basic 400,807,895 403,892,161
Effect of dilutive common share equivalents:    
Nonvested restricted shares 2,230,794 2,275,473
Stock options [1] 6,184,564 7,865,936
Weighted average common shares and common share equivalents outstanding — diluted 409,223,253 414,033,570
Earnings per common share:    
Basic (per share) $ 1.07 $ 0.33
Diluted (per share) $ 1.05 $ 0.32
Stock options    
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]    
Antidilutive securities excluded from computation of earnings per common share (shares) 2,400,082 1,155,088
[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 first quarter and 2020 first quarter, the number of stock options excluded were 2,400,082 and 1,155,088, respectively.