Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended								12 Months Ended
		Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Numerator:
Net income		$ 326,384	$ 392,453	$ 468,954	$ 448,528	$ 136,494	$ 227,408	$ 243,646	$ 150,423	$ 1,693,300	$ 727,821	$ 629,709
Net (income) loss attributable to noncontrolling interests										(56,981)	30,150	(10,431)
Net income available to Arch										1,636,319	757,971	619,278
Preferred dividends		(10,403)	(10,403)	(10,403)	(10,403)	(10,403)	(10,402)	(10,403)	(10,437)	(41,612)	(41,645)	(46,041)
Loss on redemption of preferred shares										0	(2,710)	(6,735)
Net income available to Arch common shareholders		$ 315,981	$ 382,050	$ 458,551	$ 438,125	$ 126,091	$ 217,006	$ 233,243	$ 137,276	$ 1,594,707	$ 713,616	$ 566,502
Denominator:
Weighted average common shares outstanding										401,802,815	401,036,376	377,531,628
Series D preferred securities	[1]									0	3,311,245	26,606,736
Weighted average common shares outstanding — basic										401,802,815	404,347,621	404,138,364
Effect of dilutive common share equivalents:
Nonvested restricted shares										1,673,770	1,474,207	3,936,594
Stock options	[2]									8,132,893	7,084,650	9,710,067
Weighted average common shares and common share equivalents outstanding — diluted										411,609,478	412,906,478	417,785,025
Earnings per common share:
Basic (per share)		$ 0.78	$ 0.95	$ 1.14	$ 1.09	$ 0.31	$ 0.54	$ 0.58	$ 0.34	$ 3.97	$ 1.76	$ 1.40
Diluted (per share)		$ 0.76	$ 0.92	$ 1.12	$ 1.07	$ 0.31	$ 0.53	$ 0.56	$ 0.33	$ 3.87	$ 1.73	$ 1.36
Stock Options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)										1,302,017	5,673,821	2,603,451

[1] The company has determined that, based on a review of the terms, features and rights of the Company’s non-voting common equivalent preferred shares compared to the rights of the Company’s common shareholders, the underlying common shares that the convertible securities convert to were common share equivalents at the time of their issuance.

[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 2019, 2018 and 2017, the number of stock options excluded were 1,302,017, 5,673,821 and 2,603,451, respectively.