Birthday Paradox Calculator

How to use

1. 1Enter the number of people in the group. The famous example is 23 people in a 365-day year.
2. 2Set the days in year. Use 365 for a standard year, 366 for a leap year, or any bucket count for dice, hashes, or UUIDs.
3. 3Read the match probability at the top of the result panel, with the complement (all-different probability) below it.
4. 4Check the group-size table to find the smallest group needed to hit 25%, 50%, 75%, 95%, 99%, or 99.9% probability.
5. 5Tap a Quick example to load a preset (classroom of 30, 23 people, leap year office, d20 rolls, 16-bit hash collisions).
6. 6Click Copy full result to grab a text summary with the probability, the complement, and the threshold table.

About this tool

Birthday Paradox Calculator computes the probability that at least two people in a group of n share the same birthday, for any group size and any bucket count. The default 365-day year reproduces the classic textbook result, where the probability passes 50% at just 23 people and climbs to 99% by 57 people, which feels counterintuitive because we tend to anchor on 365 and expect the answer to grow linearly with n. The math under the hood is the product form P(no match) = (1 - 1/D)(1 - 2/D)...(1 - (n-1)/D), computed in log space and summed before a single final exponentiation, which keeps the answer accurate even when n is in the thousands and the no-match probability is microscopic. The result panel reports the match probability as a percentage, a plain decimal ready to paste into a spreadsheet or notebook, and an odds form (about 1 in X) so the same number reads naturally in writeups and presentations. A group-size table shows the smallest n that crosses each common probability threshold (25%, 50%, 75%, 95%, 99%, 99.9%), so you can answer the related question, how many people do I need for a coin-flip chance of a shared birthday, without rerunning the calculator. A distribution panel previews the probability at nearby group sizes and at standard reference values (5, 10, 23, 30, 50, 100), with the active n highlighted, so the curve's shape is obvious at a glance. Because the model only assumes D equally likely buckets and independent draws, it generalises far beyond birthdays: set D to 6 for dice, 20 for a d20, 65,536 for a 16-bit hash, or any large number for hash and UUID collision estimates. Useful for statistics homework, probability lectures, party trivia, planning whether a classroom or office is likely to share a birthday, sizing how many random samples it takes before duplicates appear, and gut-checking back-of-the-envelope hash and UUID collision risks. The tool also reports the complement (P(all different)) and, when the match probability is essentially 1, expresses the gap as 1 - 10^x so you can still see meaningful digits. Everything runs in your browser. The numbers you enter never leave your device.

Free to use. Works in your browser. No signup, no login.