How many people does it take before a shared birthday is more likely than not?
Most people guess somewhere near half of 365. Try 23.
50.7%
chance at least two of them share a birthday
Explore other probability thresholds
| Odds of a shared birthday | People needed |
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It's about pairs, not dates. With 23 people there are 23×22÷2 = 253 different pairs of people. The number of possible pairs grows much faster than the number of people, so the chance of at least one match crosses 50% surprisingly quickly.
How is this calculated?
This assumes birthdays are spread evenly across 365 days (no Feb 29 and no real-world seasonal clustering), the standard simplification used in the classic problem.
P(shared) = 1 − (365 × 364 × … × (365−n+1)) / 365ⁿ, computed exactly for each n.
What changes when the number of possible comparisons grows faster than the number of things being compared?
Sources: Wolfram MathWorld — Birthday Problem;
Scientific American — Probability and the Birthday Paradox.
Standard 365-day model; leap day and real-world seasonal birthday variation are omitted.