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Earnings Per Common Share (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended
Mar. 31, 2023
Mar. 31, 2022
Numerator:    
Net income (loss) $ 717 $ 198
Amounts attributable to noncontrolling interests (2) (2)
Net income available to Arch 715 196
Preferred dividends (10) (10)
Net income (loss) available to Arch common shareholders $ 705 $ 186
Denominator:    
Weighted average common shares outstanding — basic 367.3 374.2
Effect of dilutive common share equivalents:    
Nonvested restricted shares 2.8 2.7
Stock options [1] 7.5 7.3
Weighted average common shares and common share equivalents outstanding — diluted 377.6 384.2
Earnings per common share:    
Basic (per share) $ 1.92 $ 0.50
Diluted (per share) $ 1.87 $ 0.48
Stock options    
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]    
Antidilutive securities excluded from computation of earnings per common share (shares) 0.5 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 first quarter and 2022 first quarter, the number of stock options excluded were 0.5 million and 0.8 million, respectively.