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Earnings Per Common Share (Tables)
12 Months Ended
Dec. 31, 2021
Earnings Per Share [Abstract]  
Schedule of computation of basic and diluted earnings per common share The following table sets forth the computation of basic and diluted earnings per common share:
Year Ended December 31,
202120202019
Numerator:
Net income$2,239,462 $1,465,711 $1,693,300 
Amounts attributable to noncontrolling interests(82,613)(60,190)(56,981)
Net income available to Arch2,156,849 1,405,521 1,636,319 
Preferred dividends(48,343)(41,612)(41,612)
Loss on redemption of preferred shares(15,101)— — 
Net income available to Arch common shareholders$2,093,405 $1,363,909 $1,594,707 
Denominator:
Weighted average common shares outstanding391,748,715 403,062,179 401,802,815 
Effect of dilutive common share equivalents:
Nonvested restricted shares1,996,524 1,682,309 1,673,770 
Stock options (1)6,600,697 5,514,967 8,132,893 
Weighted average common shares and common share equivalents outstanding – diluted400,345,936 410,259,455 411,609,478 
Earnings per common share:
Basic$5.34 $3.38 $3.97 
Diluted$5.23 $3.32 $3.87 
(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 2021, 2020 and 2019, the number of stock options excluded were 2,398,608, 2,249,821 and 1,302,017, respectively.