Birthday paradox
Find the chance of a shared birthday and the group size needed to reach 50%. Drag the graph handles to change inputs and explore the result.
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How it works
- Chance of at least one shared birthday = (1 − Πₖ₌₀ⁿ⁻¹(1 − k / )) × 100; Expected matching pairs = ( − 1) / (2)
- Worked example: n = 23, d = 365 ⇒ 50.72972343%; n = 22 ⇒ 47.56953077%
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Your result
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Assumptions and limitations
Birthdays are independent and uniformly distributed over the entered day count (1–10,000); this is a mathematical model, not measured demographics. The default 365 ignores leap day and seasonality. Groups contain 0–100,000 people. More people than possible days guarantee a match. Expected matching pairs can exceed one and are not a probability.
Sources
- OpenStax — birthday problem Sources reviewed: 2026-10-08
