Goodwill and Other Long-Lived Assets - Additional Information (Detail) - USD ($)				3 Months Ended												12 Months Ended
		Feb. 29, 2020	Feb. 12, 2020	Nov. 30, 2020	[1]	Aug. 31, 2020		May 31, 2020		Feb. 29, 2020		Aug. 31, 2019		May 31, 2019	Aug. 31, 2018	May 31, 2021	May 31, 2020	May 31, 2019	Jun. 01, 2019
Goodwill And Other Intangible Assets [Line Items]
Amortization expense																$ 12,257,000	$ 12,870,000	$ 15,286,000
Fixed asset net book value			$ 14,274,000
Intangible assets net book value			6,577,000
Impairment of long lived assets to be disposed of										$ 4,679,000
Impairment of goodwill and long-lived assets				$ 3,815,000		$ 9,924,000	[1]	$ 7,462,000	[1]	34,627,000	[1]	$ 40,601,000	[1]			13,739,000	82,690,000	7,817,000
Impairment of ROU assets								565,000				4,843,000
Fixed asset net book value			14,274,000
Intangible assets with net book value			$ 6,577,000
Impairment of goodwill	[2]																22,097,000
Operating lease assets								31,557,000								35,101,000	31,557,000		$ 42,200,000
Worthington Aritas
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill and long-lived assets															$ 2,381,000
Oil and Gas Equipment
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill																	22,097,000
Cryogenics
Goodwill And Other Intangible Assets [Line Items]
Impairment of long lived assets to be disposed of																3,662,000
Impairment of goodwill and long-lived assets																4,333,000
Jefferson
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill and long-lived assets																1,423,000
Superior Tools
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill and long-lived assets																506,000
TWB Hermosillo
Goodwill And Other Intangible Assets [Line Items]
Impairment of ROU assets								565,000									565,000
Packing Solutions Business
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill and long-lived assets																	2,544,000
Canton
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill and long-lived assets														$ 3,269,000
Engineered Cabs
Goodwill And Other Intangible Assets [Line Items]
Fixed asset net book value						1,469,000
Impairment of long lived assets to be disposed of												$ 35,194,000
Fixed asset net book value						1,469,000
Engineered Cabs | Stow, Ohio
Goodwill And Other Intangible Assets [Line Items]
Impairment of ROU assets						905,000
Engineered Cabs | Greensburg, Indiana
Goodwill And Other Intangible Assets [Line Items]
Operating lease assets						3,938,000
CNG Fuel Systems
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill and long-lived assets														2,167,000
Fair Value, Inputs, Level 2 | Canton
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets		$ 700,000								$ 700,000
Pressure Cylinders
Goodwill And Other Intangible Assets [Line Items]
Impairment of goodwill and long-lived assets																	3,800,000
Fair Value, Nonrecurring
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								26,984,000								400,000	26,984,000
Fair Value, Nonrecurring | Worthington Aritas
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets															$ 7,000,000
Fair Value, Nonrecurring | Fair Value, Inputs, Level 2
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								10,561,000								400,000	10,561,000
Fair Value, Nonrecurring | Fair Value, Inputs, Level 3
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								16,423,000									16,423,000
Long Lived Assets Held And Used
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								2,800,000									2,800,000
Long Lived Assets Held And Used | Jefferson
Goodwill And Other Intangible Assets [Line Items]
Carrying value long-lived assets																1,823,000
Long Lived Assets Held And Used | Packing Solutions Business
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								266,000									266,000
Carrying value long-lived assets								2,810,000									2,810,000
Long Lived Assets Held And Used | Canton
Goodwill And Other Intangible Assets [Line Items]
Carrying value long-lived assets														4,269,000
Long Lived Assets Held And Used | CNG Fuel Systems
Goodwill And Other Intangible Assets [Line Items]
Carrying value long-lived assets														2,405,000				2,405,000
Long Lived Assets Held And Used | Fair Value, Inputs, Level 2 | Cryogenics
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets																9,193,000
Carrying value long-lived assets																13,526,000
Long Lived Assets Held And Used | Fair Value, Inputs, Level 2 | Canton
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								7,813,000									7,813,000
Impairment of long lived assets to be disposed of		$ 1,274,000
Long Lived Assets Held And Used | Pressure Cylinders
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								6,600,000									6,600,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets	[3],[4],[5],[6],[7],[8]							9,277,000									9,277,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Jefferson
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets																400,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Packing Solutions Business
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets								266,000									266,000
Carrying value long-lived assets								2,810,000									2,810,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Canton
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets														1,000,000				1,000,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Engineered Cabs
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets						12,860,000
Impairment of long lived assets to be disposed of						$ 35,194,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | CNG Fuel Systems
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets														$ 238,000				$ 238,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Fair Value, Inputs, Level 2
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets	[3],[4],[5],[6],[7],[8]							6,477,000									6,477,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Fair Value, Inputs, Level 3
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets	[3],[4],[5],[6],[7],[8]							$ 2,800,000									$ 2,800,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Oil and Gas Properties
Goodwill And Other Intangible Assets [Line Items]
Fixed asset net book value																7,375,000
Intangible assets net book value																2,374,000
Impairment of long lived assets to be disposed of																1,441,000
Fixed asset net book value																7,375,000
Intangible assets with net book value																2,374,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Oil and Gas Properties | Fair Value, Inputs, Level 2
Goodwill And Other Intangible Assets [Line Items]
Fair market value of assets																5,934,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Oil and Gas Properties | Fair Value, Inputs, Level 3
Goodwill And Other Intangible Assets [Line Items]
Impairment of long lived assets to be disposed of																$ 2,374,000
Minimum [Member]
Goodwill And Other Intangible Assets [Line Items]
Definite-lived intangible assets, estimated useful lives																10 years
Maximum
Goodwill And Other Intangible Assets [Line Items]
Definite-lived intangible assets, estimated useful lives																20 years

[1] For additional information regarding the Company’s impairment activity, refer to “Note E – Goodwill and Other Long-Lived Assets.”

[2] Fiscal 2020 impairment losses included $22,097,000 of goodwill impairment related to the oil & gas equipment reporting unit.

[3] During the fourth quarter of fiscal 2020, the Company identified an impairment indicator related to the TWB Hermosillo facility operating lease due to the economic impact of COVID-19.  As a result, the lease ROU asset with a net book value of $565,000 was deemed fully impaired and written off.

[4] During the third quarter of fiscal 2020, the Company identified an impairment indicator for our oil & gas equipment business and performed an interim impairment test of the reporting unit.  In accordance with the applicable accounting guidance, the book value of the corresponding goodwill was written off, resulting in an impairment charge of $22,097,000.

[5] In May 2020, the Company committed to a plan to shut down the packaging solutions business in Greensburg, Indiana.  As a result, long-lived assets with a carrying value of $2,810,000 were written down to their estimated fair market value of $266,000.

[6] During the fourth quarter of 2020, in connection with the annual indefinite lived assets impairment test, certain European tradenames were written down to their estimated fair market value of $2,800,000.

[7] During the first quarter of fiscal 2020, the Company identified an impairment indicator for the fabricated products business in Stow, Ohio within the former Engineered Cabs operating segment.  As a result, fixed assets with a net book value of $1,469,000 and lease ROU assets with a net book value of $3,938,000 were deemed to be fully impaired and written off.

[8] During the third quarter of fiscal 2020, in connection with the closure of the oil & gas equipment operations in Wooster, Ohio, customer list intangible assets were determined to be fully impaired and written off.  In addition, the remaining fixed assets at Wooster, Ohio were written down to their estimated fair market value of $6,211,000.