Birthday paradox calculator
With just 23 people the chance that two share a birthday passes 50%; this tool works it out for any group size.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter number of people and number of possible days.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
P(all different) = (d/d) × ((d - 1)/d) × ((d - 2)/d) and so on up to ((d - n + 1)/d); P(shared) = 1 minus that, with d days in the year.
Example
Inputs: Number of people = 23, Number of possible days = 365. Result: Chance of a shared birthday: 0.5072972343; As a percentage: 50.729723%; Chance all birthdays differ: 0.4927027657.
Limits and caveats
- Assumes every day is equally likely and ignores 29 February; real births are not spread perfectly evenly.
Questions about this tool
Why are only 23 people enough?
Every pair is compared, and 23 people form 253 different pairs, which is a lot of chances.
When does the chance reach 99%?
With 57 people it is close to 99%, and with 366 a shared birthday is certain.
Is this the chance someone shares my birthday?
No, that is a different and much smaller probability; here any two people can match.