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Earnings Per Common Share (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended 6 Months Ended
Jun. 30, 2023
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Numerator:        
Net income (loss) $ 669 $ 404 $ 1,386 $ 602
Net (income) loss attributable to noncontrolling interests 2 0 0 (2)
Net income available to Arch 671 404 1,386 600
Preferred dividends (10) (10) (20) (20)
Net income (loss) available to Arch common shareholders $ 661 $ 394 $ 1,366 $ 580
Denominator:        
Weighted average common shares outstanding — basic 368.7 369.2 368.0 371.7
Effect of dilutive common share equivalents:        
Nonvested restricted shares 2.3 2.1 2.4 2.2
Stock options [1] 7.4 6.6 7.4 6.9
Weighted average common shares and common share equivalents outstanding — diluted 378.4 377.9 377.8 380.8
Earnings per common share:        
Basic (per share) $ 1.79 $ 1.07 $ 3.71 $ 1.56
Diluted (per share) $ 1.75 $ 1.04 $ 3.62 $ 1.52
Stock options        
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]        
Antidilutive securities excluded from computation of earnings per common share (shares) 0.3 0.8 0.5 0.8
[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 2023 second quarter and 2022 second quarter, the number of stock options excluded were 0.3 million and 0.8 million, respectively. For the six months ended June 30, 2023 and 2022, the number of stock options excluded were 0.5 million and 0.8 million, respectively.