Birthday paradox calculator
How many people make a shared birthday more likely than not? Explore group sizes and try a short exercise.
Inputs stay in your browser. No account or server submission.
How to use it
- Enter the number of people.
- Choose 365 or 366 equally likely days.
- Calculate the chance of any matching pair and try the exercise.
Method and example
Birthdays are assumed independent and equally likely across days. Real births vary seasonally, and 29 February is not equally common.
P(at least one pair) = 1 − ∏(1 − i/d), for i from 0 to n−1, where n is people and d is days. If n > d, the probability is 100%.
This is any pair in the group, not a match to one specified person. Displayed results are rounded.
Example: 23 people and 365 days give about 50.7297%. For 2 people the chance is 1/365, about 0.2740%.