Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2019	Sep. 30, 2018
Numerator:
Net income		$ 399,189	$ 248,766	$ 1,380,532	$ 671,497
Amounts attributable to noncontrolling interests		(6,736)	(21,358)	(70,597)	(50,020)
Net income available to Arch		392,453	227,408	1,309,935	621,477
Preferred dividends		(10,403)	(10,402)	(31,209)	(31,242)
Loss on redemption of preferred shares		0	0	0	(2,710)
Net income available to Arch common shareholders		$ 382,050	$ 217,006	$ 1,278,726	$ 587,525
Denominator:
Weighted average common shares outstanding		402,564,121	402,939,092	401,419,153	400,649,105
Series D preferred shares	[1]	0	0	0	4,427,123
Weighted average common shares outstanding — basic		402,564,121	402,939,092	401,419,153	405,076,228
Effect of dilutive common share equivalents:
Nonvested restricted shares		1,895,972	1,619,286	1,637,015	1,568,044
Stock options	[2]	8,720,108	7,162,836	7,751,234	7,348,920
Weighted average common shares and common share equivalents outstanding — diluted		413,180,201	411,721,214	410,807,402	413,993,192
Earnings per common share:
Basic (per share)		$ 0.95	$ 0.54	$ 3.19	$ 1.45
Diluted (per share)		$ 0.92	$ 0.53	$ 3.11	$ 1.42
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		37,394	4,396,352	2,198,115	5,481,584

[1] Such shares are convertible non-voting common equivalent preferred shares issued in connection with the UGC acquisition.

[2] 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 2019 third quarter and 2018 third quarter, the number of stock options excluded were 37,394 and 4,396,352, respectively. For the nine months ended September 30, 2019 and 2018 period, the number of stock options excluded were 2,198,115 and 5,481,584, respectively.