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Shareholders' equity - Purchase of Equity Securities (Details) - EUR (€) € / shares in Units, € in Millions	1 Months Ended											12 Months Ended				13 Months Ended		14 Months Ended	15 Months Ended	16 Months Ended	17 Months Ended	18 Months Ended	19 Months Ended	20 Months Ended	21 Months Ended	22 Months Ended	23 Months Ended	35 Months Ended	38 Months Ended
	Nov. 30, 2022	Oct. 31, 2022	Sep. 30, 2022	Aug. 31, 2022	Jul. 31, 2022	Jun. 30, 2022	May 30, 2022	Apr. 30, 2022	Mar. 31, 2022	Feb. 28, 2022	Jan. 31, 2022	Dec. 31, 2022	Jan. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 23, 2022	Feb. 28, 2022	Mar. 31, 2022	Apr. 30, 2022	May 31, 2022	Jun. 30, 2022	Jul. 31, 2022	Aug. 31, 2022	Sep. 30, 2022	Oct. 31, 2022	Nov. 30, 2022	Dec. 31, 2022	Dec. 31, 2022	Dec. 31, 2025
Class of Stock [Line Items]
Total number of shares purchased (in shares)	152,323	237,399	907,391	673,412	666,112	717,092	675,117	808,095	1,241,647	1,150,011	1,107,187	8,538,787	1,107,187	14,358,838		203,001	2,257,198	3,498,845	4,306,940	4,982,057	5,699,149	6,365,261	7,038,673	7,946,064	8,183,463	8,335,786	8,538,787
Treasury stock, repurchased												€ 4,639.7
Purchase of treasury shares												€ 4,639.7		€ 8,560.3	€ 1,207.5
Treasury shares, cancellation process started during the year (in shares)												3,337,825
Cancelled shares (in shares)														13,023,016
Average price paid per share (Euro per share)	€ 568.91	€ 431.23	€ 466.94	€ 541.36	€ 467.26	€ 488.27	€ 522.70	€ 573.12	€ 575.99	€ 572.80	€ 630.21	€ 543.37				€ 558.33
Maximum value of shares that may yet be purchased (€ millions)	€ 11,913.3	€ 0.0	€ 102.4	€ 526.1	€ 890.6	€ 1,201.9	€ 1,552.0	€ 1,904.9	€ 2,368.0	€ 3,083.2	€ 3,741.9					€ 11,800.0
New share buyback program
Class of Stock [Line Items]
Total number of shares purchased (in shares)												355,324
Treasury stock, repurchased												€ 200.0
Share buyback program 2020-2022
Class of Stock [Line Items]
Expected total value of purchased shares																												€ 9,000.0
Cancelled shares (in shares)												3,337,825
Forecast [Member] | Share Buyback Program 2022-2025
Class of Stock [Line Items]
Expected total value of purchased shares																													€ 12,000.0
Expected shares to be purchased for award (in shares)																													€ 2.0

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