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Earnings Per Common Share (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 6 Months Ended
Jun. 30, 2021
Jun. 30, 2020
Jun. 30, 2021
Jun. 30, 2020
Numerator:        
Net income (loss) $ 718,664 $ 466,389 $ 1,194,372 $ 377,715
Amounts attributable to noncontrolling interests (43,178) (167,568) (80,730) 65,223
Net income available to Arch 675,486 298,821 1,113,642 442,938
Preferred dividends (11,666) (10,403) (22,069) (20,806)
Net income (loss) available to Arch common shareholders $ 663,820 $ 288,418 $ 1,091,573 $ 422,132
Denominator:        
Weighted average common shares outstanding — basic 397,743,402 402,503,687 399,267,183 403,197,924
Effect of dilutive common share equivalents:        
Nonvested restricted shares 1,990,729 1,597,701 1,932,929 1,829,239
Stock options [1] 6,751,863 4,018,293 6,487,568 5,978,428
Weighted average common shares and common share equivalents outstanding — diluted 406,485,994 408,119,681 407,687,680 411,005,591
Earnings per common share:        
Basic (per share) $ 1.67 $ 0.72 $ 2.73 $ 1.05
Diluted (per share) $ 1.63 $ 0.71 $ 2.68 $ 1.03
Stock options        
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]        
Antidilutive securities excluded from computation of earnings per common share (shares) 1,974,849 6,982,107 2,395,749 2,038,758
[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 second quarter and 2020 second quarter, the number of stock options excluded were 1,974,849 and 6,982,107, respectively. For the six months ended June 30, 2021 and 2020 period, the number of stock options excluded were 2,395,749 and 2,038,758, respectively.