Birthday Paradox Calculator

Find the chance two people share a birthday.

Shared-birthday probability (%) 50.73

Formula: P = 1 − ∏(365−i)/365

Step-by-step with your numbers:
1. Values used:
2. Number of people = 23
3.
4. Shared-birthday probability = 50.73%
Did we solve your problem today?

Surprisingly few people are needed for a shared birthday to be likely.

The math behind it

P(shared) = 1 − probability all are different = 1 − ∏(365−i)/365.

Worked example

23 people → 50.7% chance of a match.

FAQ

Why so few?

It counts every pair, not just matches to one person — pairs grow fast.