Business Combinations and Acquisitions (Details) - USD ($) $ / shares in Units, $ in Millions		3 Months Ended
	Feb. 10, 2020	Sep. 27, 2020	Dec. 31, 2019
Business Acquisition [Line Items]
Common stock par value (in dollars per share)		$ 0.0001	$ 0.0001
PE Shay Holdings, LLC
Business Acquisition [Line Items]
Post-closing adjustment, payment to management		$ 20.2
PAE Management
Business Acquisition [Line Items]
Post-closing adjustment, payment to management		$ 1.0
Class A Common Stock
Business Acquisition [Line Items]
Common stock par value (in dollars per share)		$ 0.0001
Shay Holding Corporation Merger
Business Acquisition [Line Items]
Aggregate cash consideration paid	$ 424.2
Shay Holding Corporation Merger | Earn-Out Shares
Business Acquisition [Line Items]
Period following completion of business combination (in years)	5 years
Shay Holding Corporation Merger | Additional Paid-in Capital
Business Acquisition [Line Items]
Acquisition fees and expenses		$ 20.9
Shay Holding Corporation Merger | Class A Common Stock
Business Acquisition [Line Items]
Consideration paid (in shares)	21,127,823
Shay Holding Corporation Merger | Class A Common Stock | Earn-Out Shares
Business Acquisition [Line Items]
Maximum additional earn-out (in shares)	4,000,000