Only 23 People for a 50% Chance of a Shared Birthday
The Birthday Paradox is one of the most famous counterintuitive results in probability theory. Intuition says you need at least 183 people for a 50% chance of a shared birthday out of 365 days — but the real answer is just 23. That is because the number of pairs grows much faster than the number of people: 23 people create 253 pairs. Enter any group size to see the exact probability and compare it against standard reference points.
Frequently Asked Questions
P(shared) = 1 − (365/365) × (364/365) × ... × ((365−n+1)/365). This is the complement of everyone having a distinct birthday.
Yes. This calculator implements the classic birthday problem assuming uniform distribution across 365 days.
With 366 people it is guaranteed by the pigeonhole principle. In practice, 57 people already exceeds 99%.