Birthday Paradox Calculator
23 people. Better than even. Yes, really.
23 people. Better than even. Yes, really. The chance that two people in a group share a birthday, and the group sizes needed to pass 50% and 99%.
Chance two people share a birthday
50.73%
49.27% chance all 23 are different
Twenty-three people give a better-than-even chance that two share a birthday, which almost everyone finds too low. The reason is in the pairs row: 23 people form 253 pairs, and it only takes one of them to match. The intuition that fails is asking about yourself. The chance that someone shares your birthday is small and rises slowly; the chance that some pair among the group matches rises with the square of the group size. Those are different questions with very different answers. This assumes birthdays are spread evenly and ignores leap years and twins. Real birth dates cluster seasonally, which makes matches slightly more likely than the model says, not less.
How the Birthday Paradox Calculator works
The chance that two people in a group share a birthday, and the group sizes needed to pass 50% and 99%. The answer surprises almost everyone, and the pairs figure explains why in one line.
Also known as: chance two people share a birthday · why 23 people birthday · birthday problem explained · shared birthday odds in a room
Where to go next
The Birthday Paradox question rarely arrives on its own. These are the ones that usually come with it:
- Dice Probability Calculator — Exact counts, not a normal approximation that fails at the tails.
- Odds Converter — Decimal, fractional, American and the probability behind all three.
- Fibonacci Calculator — The sequence, the ratio, and where the arithmetic stops being exact.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
Why is the birthday paradox so counterintuitive?
Because people instinctively ask about themselves. The chance that someone shares your birthday rises slowly with group size; the chance that some pair among the group matches rises with the square of it. Different questions, very different answers.
How many people for a 99% chance?
Fifty-seven. It takes 366 to reach certainty by the pigeonhole principle, but the curve is steep in the middle and flat at the top, so almost all of the probability is gained early.
Does this account for leap years?
No, and real birth dates are not evenly spread either. They cluster seasonally. Both effects make matches slightly more likely than this model says, so 23 is a mild overestimate of what is needed.
Where does this matter outside parties?
Cryptography. The same mathematics governs hash collisions, and it means a hash function needs roughly twice the bits you would naively expect to resist a collision attack — the reason it is called a birthday attack.
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