STOCKHOLDERS EQUITY AND EARNINGS PER SHARE (Calculations of the Basic and Diluted Earnings Per Share) (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended
		Nov. 30, 2020	Nov. 30, 2019
Earnings Per Share [Abstract]
Earnings from continuing operations		$ 63,911	$ 82,755
Basic earnings per share:
Shares outstanding for basic earnings per share (shares)		119,762,706	118,370,191
Basic earnings per share attributable to CMC: (in USD per share)	[1]	$ 0.53	$ 0.70
Diluted earnings per share:
Shares outstanding for basic earnings per share (shares)		119,762,706	118,370,191
Effect of dilutive securities:
Stock-based incentive/purchase plans (shares)		1,365,338	1,403,347
Shares outstanding for diluted earnings per share (shares)		121,128,044	119,773,538
Diluted earnings per share attributable to CMC: (in USD per share)	[1]	$ 0.53	$ 0.69

[1] *Earnings Per Share ("EPS") is calculated independently for each component and may not sum to Net EPS due to rounding