Retirement benefits - Retirement Cost (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Pension plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	$ 2.1	$ 1.8	$ 6.8	$ 7.7
Interest cost on projected benefit obligation	8.3	9.8	24.9	28.4
Return on assets – expected	(14.9)	(14.7)	(44.8)	(43.5)
Amortization of losses	10.1	8.7	30.4	25.2
Amortization of prior service credit			(0.1)	0.0
Curtailment gain			(0.6)	0.0
Settlement loss	0.3	0.6	1.0	1.1
Net periodic pension cost	5.9	6.2	17.6	18.9
Retirement benefits other than pensions
Defined Benefit Plan Disclosure [Line Items]
Service cost			0.1	0.1
Interest cost on projected benefit obligation	3.2	4.1	9.7	12.4
Return on assets – expected	(3.1)	(3.3)	(9.2)	(9.8)
Amortization of losses	6.6	6.3	20.0	18.5
Amortization of prior service credit	(1.2)	(1.2)	(3.7)	(3.7)
Net periodic pension cost	5.5	5.9	16.9	17.5
U.S. Plans | Pension plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	0.0	0.0	0.0	0.0
Interest cost on projected benefit obligation	5.3	6.7	15.9	20.0
Return on assets – expected	(11.8)	(11.6)	(35.5)	(34.7)
Amortization of losses	8.4	7.3	25.4	21.4
Amortization of prior service credit			0.0	0.0
Curtailment gain			0.0	0.0
Settlement loss	0.0	0.0	0.0	0.0
Net periodic pension cost	1.9	2.4	5.8	6.7
Non-U.S. Plans | Pension plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	2.1	1.8	6.8	7.7
Interest cost on projected benefit obligation	3.0	3.1	9.0	8.4
Return on assets – expected	(3.1)	(3.1)	(9.3)	(8.8)
Amortization of losses	1.7	1.4	5.0	3.8
Amortization of prior service credit			(0.1)	0.0
Curtailment gain			(0.6)	0.0
Settlement loss	0.3	0.6	1.0	1.1
Net periodic pension cost	4.0	3.8	11.8	12.2
UMWA Plans | Retirement benefits other than pensions
Defined Benefit Plan Disclosure [Line Items]
Service cost			0.0	0.0
Interest cost on projected benefit obligation	2.4	3.2	7.3	9.6
Return on assets – expected	(3.1)	(3.3)	(9.2)	(9.8)
Amortization of losses	4.3	4.2	13.3	12.3
Amortization of prior service credit	(1.2)	(1.2)	(3.5)	(3.5)
Net periodic pension cost	2.4	2.9	7.9	8.6
Black Lung and Other Plans | Retirement benefits other than pensions
Defined Benefit Plan Disclosure [Line Items]
Service cost			0.1	0.1
Interest cost on projected benefit obligation	0.8	0.9	2.4	2.8
Return on assets – expected	0.0	0.0	0.0	0.0
Amortization of losses	2.3	2.1	6.7	6.2
Amortization of prior service credit	0.0	0.0	(0.2)	(0.2)
Net periodic pension cost	$ 3.1	$ 3.0	$ 9.0	$ 8.9