How fast the odds climb
The chance two people share a birthday, in groups of 2 to 100
Does your birthday change the odds?
Some birthdays are more common than others: in US births from 1989 to 2024, September 9 comes up 1.8 times as often as December 25. The more common your birthday, the fewer people it takes to find someone who shares it.
People it takes for an even chance that someone shares the date
- September 9 the most common birthday232 people
- Any day if all 365 days were equal254 people
- December 25 the rarest birthday421 people
- February 29 once in four years1,110 people
Quick answers
Why does it only take 23 people?
That is the birthday paradox: the match can be any two of them, not you and someone else. A room of 23 holds 253 pairs, and on real US births each pair shares a birthday one time in 364.5: together they pass even odds, at 50.8%. A room of 22 holds 231 pairs and falls just short, at 47.6%.
Do real birth dates change the answer?
Barely. September 9 sees 1.8 times as many births as December 25, but 355 of the 365 dates that come every year sit within 10% of an average day, so real births behave almost like equal days: 23 people for even odds, 41 for 90% and 57 for 99%, either way. The two answers are furthest apart in a room of 27, by 0.05 percentage points.
What about February 29?
The textbook answer leaves it out. Real births include it, at 1 in 1,600, and it lowers the chance a little: someone born on February 29 rarely meets a birthday twin. In a room of 23, 50.78% with it, 50.82% without.
What are the chances in a classroom of 30?
In about seven of every ten classes of 30, two children share a birthday: 70.7% on real US births, 70.6% with 365 equal days. Classmates are mostly born within the same twelve months, and in any one year the dates that fall on a weekend see fewer births, which nudges it up: on 2024's births alone it is 71.6%.