Guarantor Financial Information (Condensed Consolidating Balance Sheets) (Details) - USD ($) $ in Millions	Mar. 31, 2017	Dec. 31, 2016	Mar. 31, 2016	Dec. 31, 2015
Current assets:
Cash and cash equivalents	$ 1,322.5	$ 1,714.7	$ 612.9	$ 736.8
Accounts and notes receivable, net	2,199.4	2,223.0
Inventories, net	1,599.7	1,385.8
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	292.4	255.8
Due from Affiliate, Current	0.0	0.0
Total current assets	5,414.0	5,579.3
Property, plant and equipment, net	1,497.7	1,511.0
Intangible assets, net	9,452.1	9,443.5
Other noncurrent assets	895.7	863.6
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	17,259.5	17,397.4
Current liabilities:
Current liabilities:	3,172.8	3,229.5
Short-term borrowings and current maturities of long-term debt	361.3	360.8
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Total current liabilities	3,534.1	3,590.3
Long-term debt	3,711.1	3,709.4
Other noncurrent liabilities	3,360.4	3,379.4
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	10,605.6	10,679.1
Equity:
Total equity	6,653.9	6,718.3	5,852.7	5,879.2
Total liabilities and equity	17,259.5	17,397.4
IR Ireland [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	0.4	0.2
Due from Affiliate, Current	70.4	122.3
Total current assets	70.9	122.5
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.2	0.2
Investments in and Advances to Affiliates, at Fair Value	7,792.7	7,588.1
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	7,863.8	7,710.8
Current liabilities:
Current liabilities:	6.9	7.7
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	1,273.1	1,059.3
Total current liabilities	1,280.0	1,067.0
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	1,280.0	1,067.0
Equity:
Total equity	6,583.8	6,643.8
Total liabilities and equity	7,863.8	7,710.8
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	0.0
Total current assets	0.0	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	1,582.8	1,500.4
Due from Affiliate, Noncurrent	12,560.2	12,560.2
Total assets	14,143.0	14,060.6
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	0.0	0.0
Total current liabilities	0.0	0.0
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	0.0	0.0
Equity:
Total equity	14,143.0	14,060.6
Total liabilities and equity	14,143.0	14,060.6
IR Lux International [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	5.3	5.3
Due from Affiliate, Current	5.8	5.6
Total current assets	11.1	10.9
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	2,241.5	3,267.1
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	2,252.6	3,278.0
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	2,260.5	3,400.1
Total current liabilities	2,260.7	3,400.3
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	6,376.3	6,376.3
Total liabilities	8,637.0	9,776.6
Equity:
Total equity	(6,384.4)	(6,498.6)
Total liabilities and equity	2,252.6	3,278.0
IR Global [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	0.4	11.4
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.8	0.7
Due from Affiliate, Current	199.6	271.6
Total current assets	200.4	272.3
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	304.9	262.4
Investments in and Advances to Affiliates, at Fair Value	7,298.4	7,270.2
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	7,803.7	7,804.9
Current liabilities:
Current liabilities:	35.8	36.3
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	1,071.5	1,068.2
Total current liabilities	1,107.3	1,104.5
Long-term debt	2,287.7	2,286.3
Other noncurrent liabilities	20.6	18.2
Due to Affiliate, Noncurrent	1,817.2	1,817.2
Total liabilities	5,232.8	5,226.2
Equity:
Total equity	2,570.9	2,578.7
Total liabilities and equity	7,803.7	7,804.9
IR New Jersey [Member]
Current assets:
Cash and cash equivalents	563.9	634.6	0.0	0.0
Accounts and notes receivable, net	150.4	171.0
Inventories, net	162.1	165.3
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	102.2	69.4
Due from Affiliate, Current	504.0	220.5
Total current assets	1,482.6	1,260.8
Property, plant and equipment, net	442.5	445.9
Intangible assets, net	412.7	414.7
Other noncurrent assets	718.3	676.3
Investments in and Advances to Affiliates, at Fair Value	15,425.8	15,273.4
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	18,481.9	18,071.1
Current liabilities:
Current liabilities:	515.8	525.1
Short-term borrowings and current maturities of long-term debt	350.4	350.4
Short-term borrowings and current maturities of long-term debt	6,701.9	6,285.6
Total current liabilities	7,568.1	7,161.1
Long-term debt	334.2	334.2
Other noncurrent liabilities	1,256.5	1,280.8
Due to Affiliate, Noncurrent	2,034.6	2,034.6
Total liabilities	11,193.4	10,810.7
Equity:
Total equity	7,288.5	7,260.4
Total liabilities and equity	18,481.9	18,071.1
IR Lux Finance [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	0.1	0.1
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	0.0	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	1,109.3	1,090.4
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	1,109.3	1,090.4
Current liabilities:
Current liabilities:	16.9	7.0
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	477.2	486.9
Total current liabilities	494.1	493.9
Long-term debt	1,088.6	1,088.3
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	1,582.7	1,582.2
Equity:
Total equity	(473.4)	(491.8)
Total liabilities and equity	1,109.3	1,090.4
Other Subsidiaries [Member]
Current assets:
Cash and cash equivalents	758.5	1,080.1	612.4	725.3
Accounts and notes receivable, net	2,049.0	2,052.0
Inventories, net	1,437.6	1,220.5
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	189.6	189.3
Due from Affiliate, Current	11,082.1	11,747.9
Total current assets	15,516.8	16,289.8
Property, plant and equipment, net	1,055.2	1,065.1
Intangible assets, net	9,039.4	9,028.8
Other noncurrent assets	623.7	580.1
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	3,851.8	3,851.8
Total assets	30,086.9	30,815.6
Current liabilities:
Current liabilities:	2,603.1	2,662.3
Short-term borrowings and current maturities of long-term debt	10.9	10.4
Short-term borrowings and current maturities of long-term debt	77.8	67.8
Total current liabilities	2,691.8	2,740.5
Long-term debt	0.6	0.6
Other noncurrent liabilities	2,834.7	2,735.8
Due to Affiliate, Noncurrent	6,183.9	6,183.9
Total liabilities	11,711.0	11,660.8
Equity:
Total equity	18,375.9	19,154.8
Total liabilities and equity	30,086.9	30,815.6
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	(5.9)	(9.1)
Due from Affiliate, Current	(11,861.9)	(12,367.9)
Total current assets	(11,867.8)	(12,377.0)
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	(751.4)	(655.4)
Investments in and Advances to Affiliates, at Fair Value	(35,450.5)	(35,989.6)
Due from Affiliate, Noncurrent	(16,412.0)	(16,412.0)
Total assets	(64,481.7)	(65,434.0)
Current liabilities:
Current liabilities:	(5.9)	(9.1)
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	(11,862.0)	(12,367.9)
Total current liabilities	(11,867.9)	(12,377.0)
Long-term debt	0.0	0.0
Other noncurrent liabilities	(751.4)	(655.4)
Due to Affiliate, Noncurrent	(16,412.0)	(16,412.0)
Total liabilities	(29,031.3)	(29,444.4)
Equity:
Total equity	(35,450.4)	(35,989.6)
Total liabilities and equity	$ (64,481.7)	$ (65,434.0)