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Birthday Paradox Calculator

How likely is a shared birthday in a group?

Chance of any shared birthday

50.73%

Reference points

  • 10 people: 11.7%
  • 23 people: 50.7%
  • 30 people: 70.6%
  • 50 people: 97.0%
  • 70 people: 99.9%
  • 100 people: 99.99997%

About

Enter a group size and see the probability that at least two people share a birthday. The math surprises most people: in a room of 23, it's already over 50%. In 70, it's 99.9%.

How to use

  1. Enter the number of people.
  2. See the probability of any shared birthday.

FAQ

Why is the answer so high?+

Because you're not asking 'does someone share my birthday?' You're asking 'does any pair share?' With n people there are n × (n-1) / 2 pairs, which grows quadratically. Surprises happen at small n.