Acquisitions - Narrative (Details) $ in Millions				12 Months Ended
	Sep. 06, 2018 USD ($) customer	Jul. 27, 2018 USD ($)	Jun. 06, 2018 USD ($)	Dec. 31, 2018 USD ($) acquisition business	Dec. 31, 2017 USD ($) business	Dec. 31, 2016 USD ($) business
Business Acquisition [Line Items]
Goodwill				$ 6,133.1	$ 4,560.3	$ 3,445.1
Accruent
Business Acquisition [Line Items]
Total purchase price	$ 1,993.4
Number of customers served | customer	10,000
Revenue of prior fiscal year				200.0
Goodwill	$ 1,141.0
Gordian
Business Acquisition [Line Items]
Total purchase price		$ 778.1
Revenue of prior fiscal year				110.0
Goodwill		$ 428.9
Other
Business Acquisition [Line Items]
Total purchase price				43.6
Revenue of prior fiscal year				35.0
Goodwill				$ 31.3
Number of businesses acquired | business				2
2018 Acquisitions
Business Acquisition [Line Items]
Total purchase price				$ 2,815.1
Goodwill				1,601.2
Revenue from acquiree since acquisition date				115.0
Operating income (loss) since acquisition				(51.0)
Transaction costs				$ 25.0
Number of acquisitions | acquisition				4
Goodwill, purchase accounting adjustments				$ 61.0
2017 Acquisitions
Business Acquisition [Line Items]
Total purchase price					1,556.6
Revenue of prior fiscal year					389.0
Goodwill					$ 1,035.2
Number of businesses acquired | business					3
Transaction costs					$ 19.0
2016 Acquisitions
Business Acquisition [Line Items]
Total purchase price						190.1
Revenue of prior fiscal year						47.0
Goodwill						$ 113.2
Number of businesses acquired | business						3
ASP
Business Acquisition [Line Items]
Total purchase price			$ 2,700.0