What this calculator does
Birthday paradox probability works out chance that at least two people in a group share the same birthday. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaP(match) = 1 − d(d−1)(d−2)…(d−n+1) / dⁿ, with d possible days
The inputs explained
| Field | What to enter |
|---|---|
| Number of people | A number. Starts at 23. |
| Possible birthdays (days) | A number. Starts at 365. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with number of people
Every other input is held at the calculator’s starting values while number of people varies. Select any row to load that scenario into the calculator.