Why 23 people is enough
The chance that no two people share a birthday shrinks with every pair, and pairs multiply quickly: 23 people make 253 pairs. With real U.S. birth frequencies, a group of 23 has a 50.8% chance of at least one shared birthday; at 57 people it is 99.0%, and at 70 it is 99.9%.
Real birthdays are uneven
Textbook answers assume 365 equally likely days. Real births are not spread evenly: more fall in late summer, fewer on holidays, and February 29 occurs only once every four years. Uneven dates make matches slightly more likely, so each group’s chance is a little higher than the textbook figure, 50.8% against 50.7% at 23. This calculator uses each date’s share of 62,187,024 U.S. births from 2000 to 2014.
Sharing your own birthday
Matching one particular date is far harder. You would need about 253 other people for an even chance of someone sharing your birthday if all days were equal. With real data it takes 226 people for September 12, the most common birthday, 447 for December 25 and 1,030 for February 29. See how common your own date is on the birthday heatmap.
How it is calculated
For each group size, the chance that everyone’s birthday differs is calculated exactly from the 366 date shares; one minus that is the chance of a shared birthday. Nothing you enter leaves the page. Counts come from SSA records compiled by FiveThirtyEight (CC BY 4.0).
Good questions
What is the birthday paradox?
It is the surprise that a small group is likely to contain two people with the same birthday: with 23 people the chance passes 50%. It feels wrong because we think of our own birthday, but 23 people form 253 pairs, and any pair can match.
How many people do you need for a 50% chance of a shared birthday?
23. With real U.S. birth frequencies the chance is 50.8%; the textbook 365-day formula gives 50.7%. With 22 people it is just under half.
What is the birthday problem?
The same question stated as a probability problem: how many people are needed before a shared birthday becomes likely? This calculator answers it for any group from 2 to 100 people.
What are the odds someone shares my birthday?
Much lower, because only your date counts: you need about 253 other people for an even chance with 365 equal days. With real data it takes 226 for September 12, the most common birthday, 447 for December 25 and 1,030 for February 29.