Twenty-three people, even odds
Calculates the chance that two people in a group share a birthday, and how many people are needed for a 50 or 99 percent chance.
The result feels wrong: in a group of 23 there is already a better than even chance that two of them share a birthday. The intuition that goes wrong is comparing everyone with yourself.
The question is about any pair. Twenty-three people make 253 pairs, and it only takes one of them to match. That is why the probability climbs so much faster than the group size.
What this calculator shows
- The chance that at least two people share a date
- The number of pairs in the group
- How many people are needed for a 50 and a 99 percent chance
What to keep in mind
- Birthdays are treated as spread evenly across the year, and 29 February is ignored.
- Real birthdays cluster slightly by season, which makes matches marginally more likely than the model says.
FAQs
Why 23 and not 183?
Because 183 answers a different question — sharing with one specific person. Any pair matching is a much easier condition, and 23 people already give 253 chances.
What is the chance someone shares my birthday?
About 6 percent in a group of 23, and it needs 253 people to pass even odds. That is the intuition most people are actually using.
Does 29 February change anything?
Almost nothing. Adding a day that occurs a quarter as often shifts the answer by a fraction of a percent.
Where else does this come up?
In cryptography. The same maths says a hash of n bits starts producing collisions after about 2^(n/2) values, which is why 64-bit hashes are not used for security.
Worked example
A group of 23
Input: 23 people, 365 days
Output: 50.7 percent
Note: At 57 people it passes 99 percent. The chance that someone shares your birthday specifically is only about 6 percent in a group of 23 — a completely different question.