Guarantor Financial Information (Condensed Consolidating Balance Sheets) (Details) - USD ($) $ in Millions	Jun. 30, 2018	Dec. 31, 2017	Jun. 30, 2017	Dec. 31, 2016
Current assets:
Cash and cash equivalents	$ 969.5	$ 1,549.4	$ 1,310.1	$ 1,714.7
Accounts and notes receivable, net	2,946.9	2,477.4
Inventories, net	1,733.3	1,555.4
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	512.0	536.9
Due from Affiliate, Current	0.0	0.0
Total current assets	6,161.7	6,119.1
Property, plant and equipment, net	1,646.8	1,551.3
Intangible assets, net	9,706.0	9,678.6
Other noncurrent assets	863.4	824.3
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	0.0
Total assets	18,377.9	18,173.3
Current liabilities:
Current liabilities:	4,153.1	3,721.0
Short-term borrowings and current maturities of long-term debt	599.6	1,107.0
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Total current liabilities	4,752.7	4,828.0
Long-term debt	3,738.9	2,957.0
Other noncurrent liabilities	3,062.6	3,181.4
Due to Affiliate, Noncurrent	0.0
Total liabilities	11,554.2	10,966.4
Equity:
Total equity	6,823.7	7,206.9	6,794.0	6,718.3
Total liabilities and equity	18,377.9	18,173.3
IR Ireland [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	0.0	0.0
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.2	0.2
Due from Affiliate, Current	27.8	1,819.1
Total current assets	28.0	1,819.3
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.0	0.0
Investments in and Advances to Affiliates, at Fair Value	8,672.2	7,318.1
Due from Affiliate, Noncurrent	0.0
Total assets	8,700.2	9,137.4
Current liabilities:
Current liabilities:	140.7	8.5
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	1,772.4	1,988.3
Total current liabilities	1,913.1	1,996.8
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.3
Due to Affiliate, Noncurrent	0.0
Total liabilities	1,913.1	1,997.1
Equity:
Total equity	6,787.1	7,140.3
Total liabilities and equity	8,700.2	9,137.4
IR Irish Holdings [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	0.0	0.0
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.0	0.0
Due from Affiliate, Current	0.0	9,912.2
Total current assets	0.0	9,912.2
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.0	0.0
Investments in and Advances to Affiliates, at Fair Value	8,633.1	1,684.2
Due from Affiliate, Noncurrent	0.0
Total assets	8,633.1	11,596.4
Current liabilities:
Current liabilities:	0.0	0.0
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	2.5	0.0
Total current liabilities	2.5	0.0
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0
Total liabilities	2.5	0.0
Equity:
Total equity	8,630.6	11,596.4
Total liabilities and equity	8,633.1	11,596.4
IR Lux International [Member]
Current assets:
Cash and cash equivalents	0.7	0.6	0.1	0.0
Accounts and notes receivable, net	0.2	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	7.9	5.7
Due from Affiliate, Current	313.1	2,036.8
Total current assets	321.9	2,043.1
Property, plant and equipment, net	0.1	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	4.0	0.0
Investments in and Advances to Affiliates, at Fair Value	3,233.3	2,953.9
Due from Affiliate, Noncurrent	1,000.0
Total assets	4,559.3	4,997.0
Current liabilities:
Current liabilities:	0.2	0.2
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	843.2	9,316.7
Total current liabilities	843.4	9,316.9
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0
Total liabilities	843.4	9,316.9
Equity:
Total equity	3,715.9	(4,319.9)
Total liabilities and equity	4,559.3	4,997.0
IR Global [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	0.0	0.0
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	11.7	112.6
Due from Affiliate, Current	0.0	0.0
Total current assets	11.7	112.6
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	187.2	185.4
Investments in and Advances to Affiliates, at Fair Value	11,061.9	10,480.3
Due from Affiliate, Noncurrent	0.0
Total assets	11,260.8	10,778.3
Current liabilities:
Current liabilities:	80.1	27.3
Short-term borrowings and current maturities of long-term debt	0.0	749.6
Short-term borrowings and current maturities of long-term debt	3,356.3	5,481.1
Total current liabilities	3,436.4	6,258.0
Long-term debt	2,328.8	1,539.9
Other noncurrent liabilities	66.8	92.4
Due to Affiliate, Noncurrent	2,249.7
Total liabilities	8,081.7	7,890.3
Equity:
Total equity	3,179.1	2,888.0
Total liabilities and equity	11,260.8	10,778.3
IR New Jersey [Member]
Current assets:
Cash and cash equivalents	0.0	359.3	589.0	634.6
Accounts and notes receivable, net	169.3	166.5
Inventories, net	161.5	168.5
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	109.1	76.2
Due from Affiliate, Current	2,278.2	1,849.9
Total current assets	2,718.1	2,620.4
Property, plant and equipment, net	321.5	310.6
Intangible assets, net	432.0	436.0
Other noncurrent assets	437.6	471.1
Investments in and Advances to Affiliates, at Fair Value	11,552.4	10,923.7
Due from Affiliate, Noncurrent	0.0
Total assets	15,461.6	14,761.8
Current liabilities:
Current liabilities:	538.1	572.3
Short-term borrowings and current maturities of long-term debt	350.4	350.4
Short-term borrowings and current maturities of long-term debt	2,015.3	1,790.0
Total current liabilities	2,903.8	2,712.7
Long-term debt	319.4	326.8
Other noncurrent liabilities	1,186.5	1,251.8
Due to Affiliate, Noncurrent	0.0
Total liabilities	4,409.7	4,291.3
Equity:
Total equity	11,051.9	10,470.5
Total liabilities and equity	15,461.6	14,761.8
IR Lux Finance [Member]
Current assets:
Cash and cash equivalents	0.1	0.0	0.0	0.0
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.0	0.0
Due from Affiliate, Current	0.0	0.0
Total current assets	0.1	0.0
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.0	0.0
Investments in and Advances to Affiliates, at Fair Value	1,191.4	1,150.9
Due from Affiliate, Noncurrent	0.0
Total assets	1,191.5	1,150.9
Current liabilities:
Current liabilities:	6.9	6.9
Short-term borrowings and current maturities of long-term debt	249.0	0.0
Short-term borrowings and current maturities of long-term debt	299.7	523.3
Total current liabilities	555.6	530.2
Long-term debt	1,090.4	1,089.7
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0
Total liabilities	1,646.0	1,619.9
Equity:
Total equity	(454.5)	(469.0)
Total liabilities and equity	1,191.5	1,150.9
Other Subsidiaries [Member]
Current assets:
Cash and cash equivalents	968.7	1,189.5	721.0	1,080.1
Accounts and notes receivable, net	2,777.4	2,310.9
Inventories, net	1,571.8	1,386.9
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	383.6	342.2
Due from Affiliate, Current	5,707.5	5,014.8
Total current assets	11,409.0	10,244.3
Property, plant and equipment, net	1,325.2	1,240.7
Intangible assets, net	9,274.0	9,242.6
Other noncurrent assets	610.2	550.8
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	1,249.7
Total assets	23,868.1	21,278.4
Current liabilities:
Current liabilities:	3,387.6	3,105.8
Short-term borrowings and current maturities of long-term debt	0.2	7.0
Short-term borrowings and current maturities of long-term debt	37.2	1,533.4
Total current liabilities	3,425.0	4,646.2
Long-term debt	0.3	0.6
Other noncurrent liabilities	2,184.9	2,219.9
Due to Affiliate, Noncurrent	0.0
Total liabilities	5,610.2	6,866.7
Equity:
Total equity	18,257.9	14,411.7
Total liabilities and equity	23,868.1	21,278.4
Consolidation, Eliminations [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	$ 0.0	$ 0.0
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	(0.5)	0.0
Due from Affiliate, Current	(8,326.6)	(20,632.8)
Total current assets	(8,327.1)	(20,632.8)
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	(375.6)	(383.0)
Investments in and Advances to Affiliates, at Fair Value	(44,344.3)	(34,511.1)
Due from Affiliate, Noncurrent	(2,249.7)
Total assets	(55,296.7)	(55,526.9)
Current liabilities:
Current liabilities:	(0.5)	0.0
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	(8,326.6)	(20,632.8)
Total current liabilities	(8,327.1)	(20,632.8)
Long-term debt	0.0	0.0
Other noncurrent liabilities	(375.6)	(383.0)
Due to Affiliate, Noncurrent	(2,249.7)
Total liabilities	(10,952.4)	(21,015.8)
Equity:
Total equity	(44,344.3)	(34,511.1)
Total liabilities and equity	$ (55,296.7)	$ (55,526.9)