Discontinued Operations (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2020	Sep. 30, 2019	Dec. 31, 2019
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Deconsolidation, Gain (Loss), Amount			$ 22.7
Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent	$ (5.5)	$ 76.2	(121.3)	$ 178.9
Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Noncontrolling Interest	0.0	(0.9)	(0.9)	(2.3)
Discontinued operations, net of tax	(5.5)	77.1	(120.4)	181.2
Disposal Group, Including Discontinued Operation, Assets, Current					$ 1,130.6
Disposal Group, Including Discontinued Operation, Revenue	0.0	873.4	469.8	2,555.8
Disposal Group, Including Discontinued Operation, Costs of Goods Sold	0.0	(569.2)	(315.8)	(1,728.6)
Disposal Group, Including Discontinued Operation, General and Administrative Expense	(0.3)	(217.5)	(234.4)	(574.9)
Disposal Group, Including Discontinued Operation, Operating Income (Loss)	(0.3)	86.7	(80.4)	252.3
Disposal Group, Including Discontinued Operation, Other Expense	7.4	30.6	50.7	21.1
Discontinued Operation, Income (Loss) from Discontinued Operation, before Income Tax	(7.7)	117.3	(131.1)	273.4
Discontinued Operation, Tax Effect of Discontinued Operation	(2.2)	40.2	(10.7)	92.2
Disposal Group, Including Discontinued Operation, Property, Plant and Equipment, Noncurrent					454.3
Disposal Group, Including Discontinued Operation, Goodwill					1,657.4
Disposal Group, Including Discontinued Operation, Intangible Assets					825.2
Disposal Group, Including Discontinued Operation, Assets, Noncurrent					139.7
Disposal Group, Including Discontinued Operation, Assets	0.0		0.0		4,207.2
Disposal Group, Including Discontinued Operation, Liabilities, Current					823.7
Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent					376.7
Disposal Group, Including Discontinued Operation, Liabilities	0.0		0.0		1,200.4
IndustrialSegmentBusinesses [Domain]
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Separation costs	2.3	29.0	113.9	45.1
Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent	(0.5)	51.8	(83.0)	162.2
Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Noncontrolling Interest	0.0	0.9	0.9	2.3
Discontinued operations, net of tax	(0.5)	52.7	(82.1)	164.5
Separation costs, net of tax	1.8	28.3	95.9	44.4
Cash and Cash Equivalents [Member]
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Disposal Group, Including Discontinued Operation, Assets, Current					$ 25.0
Discontinued Operations [Member]
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Deconsolidation, Gain (Loss), Amount, net of tax	16.9
Discontinued Operations [Member] | Trane Technologies Company LLC [Member]
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Deconsolidation, Gain (Loss), Amount			23.6
Other Discontinued Operations [Member]
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Discontinued operations, net of tax	$ (5.0)	$ 24.4	$ (38.3)	$ 16.7