Guarantor Financial Information (Condensed Consolidating Balance Sheets) (Details) - USD ($) $ in Millions	Sep. 30, 2016	Dec. 31, 2015	Sep. 30, 2015	Dec. 31, 2014
Current assets:
Cash and cash equivalents	$ 1,504.6	$ 736.8	$ 651.5	$ 1,705.2
Accounts and notes receivable, net	2,360.8	2,150.6
Inventories, net	1,556.0	1,410.7
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	293.1	311.3
Due from Affiliate, Current	0.0	0.0
Total current assets	5,714.5	4,609.4
Property, plant and equipment, net	1,548.9	1,575.1
Intangible assets, net	9,604.3	9,656.3
Other noncurrent assets	852.2	876.8
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	17,719.9	16,717.6
Current liabilities:
Current liabilities:	3,342.4	3,144.2
Short-term borrowings and current maturities of long-term debt	361.0	504.2
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Total current liabilities	3,703.4	3,648.4
Long-term debt	3,708.9	3,713.6
Other noncurrent liabilities	3,476.5	3,476.4
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	10,888.8	10,838.4
Equity:
Total equity	6,831.1	5,879.2	5,796.7	6,045.4
Total liabilities and equity	17,719.9	16,717.6
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	0.1
Due from Affiliate, Current	201.3	136.8
Total current assets	201.5	136.9
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	12,219.5	10,139.0
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	12,421.2	10,276.1
Current liabilities:
Current liabilities:	6.3	7.1
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	5,650.8	4,452.3
Total current liabilities	5,657.1	4,459.4
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	5,657.1	4,459.4
Equity:
Total equity	6,764.1	5,816.7
Total liabilities and equity	12,421.2	10,276.1
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	1,155.1	20,387.2
Due from Affiliate, Noncurrent	18,048.4	0.0
Total assets	19,203.5	20,387.2
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	143.6
Total current liabilities	0.0	143.6
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	143.6
Equity:
Total equity	19,203.5	20,243.6
Total liabilities and equity	19,203.5	20,387.2
IR Lux International [Member]
Current assets:
Cash and cash equivalents	0.1	0.0	0.0	1.1
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	5.4	0.0
Due from Affiliate, Current	5.5	3.3
Total current assets	11.0	3.3
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	15,056.1	13,419.7
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	15,067.1	13,423.0
Current liabilities:
Current liabilities:	0.2	0.1
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	4,029.2	23,529.0
Total current liabilities	4,029.4	23,529.1
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.3	0.0
Due to Affiliate, Noncurrent	18,048.4	0.0
Total liabilities	22,078.1	23,529.1
Equity:
Total equity	(7,011.0)	(10,106.1)
Total liabilities and equity	15,067.1	13,423.0
IR Global [Member]
Current assets:
Cash and cash equivalents	0.0	11.4	0.0	0.0
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	10.4	6.4
Due from Affiliate, Current	340.6	102.2
Total current assets	351.0	120.0
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	267.9	283.8
Investments in and Advances to Affiliates, at Fair Value	7,252.8	6,438.1
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	7,871.7	6,841.9
Current liabilities:
Current liabilities:	55.5	30.7
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	1,064.9	1,997.8
Total current liabilities	1,120.4	2,028.5
Long-term debt	2,286.1	2,284.4
Other noncurrent liabilities	24.7	8.3
Due to Affiliate, Noncurrent	1,817.2	429.0
Total liabilities	5,248.4	4,750.2
Equity:
Total equity	2,623.3	2,091.7
Total liabilities and equity	7,871.7	6,841.9
IR New Jersey [Member]
Current assets:
Cash and cash equivalents	541.3	0.0	0.0	425.4
Accounts and notes receivable, net	170.7	160.7
Inventories, net	202.2	192.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	105.3	83.3
Due from Affiliate, Current	244.7	1,413.4
Total current assets	1,264.2	1,849.4
Property, plant and equipment, net	454.1	463.0
Intangible assets, net	418.8	411.6
Other noncurrent assets	713.7	733.4
Investments in and Advances to Affiliates, at Fair Value	15,050.1	13,925.1
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	17,900.9	17,382.5
Current liabilities:
Current liabilities:	587.6	597.6
Short-term borrowings and current maturities of long-term debt	350.4	350.4
Short-term borrowings and current maturities of long-term debt	6,060.9	5,858.1
Total current liabilities	6,998.9	6,806.1
Long-term debt	334.2	341.6
Other noncurrent liabilities	1,295.5	1,367.9
Due to Affiliate, Noncurrent	2,034.6	2,447.7
Total liabilities	10,663.2	10,963.3
Equity:
Total equity	7,237.7	6,419.2
Total liabilities and equity	17,900.9	17,382.5
IR Lux Finance [Member]
Current assets:
Cash and cash equivalents	0.1	0.1	0.2	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	0.1
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	1,689.7	1,583.2
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	1,689.8	1,583.3
Current liabilities:
Current liabilities:	17.1	6.3
Short-term borrowings and current maturities of long-term debt	0.0	143.0
Short-term borrowings and current maturities of long-term debt	670.7	745.5
Total current liabilities	687.8	894.8
Long-term debt	1,088.0	1,086.9
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	1,775.8	1,981.7
Equity:
Total equity	(86.0)	(398.4)
Total liabilities and equity	1,689.8	1,583.3
Other Subsidiaries [Member]
Current assets:
Cash and cash equivalents	963.1	725.3	651.3	1,278.7
Accounts and notes receivable, net	2,190.1	1,989.9
Inventories, net	1,353.8	1,218.7
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	201.6	237.5
Due from Affiliate, Current	16,754.2	35,404.3
Total current assets	21,462.8	39,575.7
Property, plant and equipment, net	1,094.8	1,112.1
Intangible assets, net	9,185.5	9,244.7
Other noncurrent assets	562.1	568.4
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	3,851.8	2,876.7
Total assets	36,157.0	53,377.6
Current liabilities:
Current liabilities:	2,705.5	2,518.3
Short-term borrowings and current maturities of long-term debt	10.6	10.8
Short-term borrowings and current maturities of long-term debt	70.1	334.0
Total current liabilities	2,786.2	2,863.1
Long-term debt	0.6	0.7
Other noncurrent liabilities	2,847.9	2,809.1
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	5,634.7	5,672.9
Equity:
Total equity	30,522.3	47,704.7
Total liabilities and equity	36,157.0	53,377.6
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	(29.8)	(16.0)
Due from Affiliate, Current	(17,546.3)	(37,060.0)
Total current assets	(17,576.1)	(37,076.0)
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	(691.7)	(709.0)
Investments in and Advances to Affiliates, at Fair Value	(52,423.3)	(65,892.3)
Due from Affiliate, Noncurrent	(21,900.2)	(2,876.7)
Total assets	(92,591.3)	(106,554.0)
Current liabilities:
Current liabilities:	(29.8)	(15.9)
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	(17,546.6)	(37,060.3)
Total current liabilities	(17,576.4)	(37,076.2)
Long-term debt	0.0	0.0
Other noncurrent liabilities	(691.9)	(708.9)
Due to Affiliate, Noncurrent	(21,900.2)	(2,876.7)
Total liabilities	(40,168.5)	(40,661.8)
Equity:
Total equity	(52,422.8)	(65,892.2)
Total liabilities and equity	$ (92,591.3)	$ (106,554.0)