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Birthday / Miracle Calculator

Birthday collision probability — how surprising is a shared birthday?

Mode

Parameters

Group size (k)Slots / days (d)Threshold target %

Results

P(shared birthday)

50.73%

People for 50% chance

23

Group size

23

Slots

365

Probability curve (first 40 group sizes)

n = 1

n = 3

0.82%

n = 5

2.71%

n = 7

5.62%

n = 9

9.46%

n = 11

14.11%

n = 13

19.44%

n = 15

25.29%

n = 17

31.5%

n = 19

37.91%

n = 21

44.37%

n = 23

50.73%

n = 25

56.87%

n = 27

62.69%

n = 29

68.1%

n = 31

73.05%

n = 33

77.5%

n = 35

81.44%

n = 37

84.87%

n = 39

87.82%

Why it's surprising: With 23 people and 365 days, there is already a ~50.7% chance two share a birthday. The birthday "paradox" is really about how quickly coincidences accumulate in groups — we underestimate the number of pairs (23 people = 253 pairs).

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