Birthday Paradox Calculator
Explore the birthday paradox — the surprising probability that two people share a birthday.
A famously counterintuitive result
The birthday paradox is the surprising fact that in a fairly small group of people, the chance that two share a birthday is much higher than intuition suggests. This calculates that probability for any group size, letting you see the effect for yourself.
Enter a group size to see the probability of a shared birthday.
Why it feels wrong but isn't
Most people guess you would need a huge group for a shared birthday to be likely, but in fact it takes only about 23 people for the odds to pass fifty percent, and around 70 people makes it nearly certain. The reason intuition fails is that we instinctively think about our own birthday matching someone else's, when the question is whether any two people among the group match — and the number of possible pairs grows very fast as the group grows, far faster than the group itself. With 23 people there are already 253 possible pairs, each a chance of a match. It is a perfect example of how probability defies gut feeling, and why counting the possibilities carefully beats guessing.
Questions & answers
How many people are needed for a fifty percent chance of a shared birthday?
Only about 23 — far fewer than most people expect — and around 70 makes a shared birthday nearly certain.
Why is the result so counterintuitive?
Because we think about matching our own birthday, but the question is whether any two of the group match, and the number of possible pairs grows very fast.
Is anything uploaded?
No. The calculation happens in your browser.