The result surprises people because the number of possible pairs grows quickly: 23 people form 253 pairs.
How to use the Birthday Paradox Calculator
- Number of people
- Days in year
- Want to work backwards? Type a value into Chance of a shared birthday and Number of people is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
The calculator computes the chance that all birthdays differ using log-gamma, then subtracts from 1.
Inputs explained
| Field | What to enter |
|---|---|
| Number of people | A number |
| Days in year | A number |
Example values
How the main result changes when Number of people changes and everything else stays at the example values above:
| Number of people | Chance of a shared birthday (%) |
|---|---|
| 11.5 | 15.388 |
| 17.25 | 32.294 |
| 23 | 50.73 |
| 28.75 | 67.445 |
| 34.5 | 80.501 |
| 46 | 94.825 |
Formula
P(shared) = 1 − 365! ÷ ((365 − n)! × 365ⁿ)Worked example
Inputs — Number of people: 23; Days in year: 365.
Results — Chance of a shared birthday = 50.73 %; Number of pairs = 253.
Frequently asked questions
Does this ignore leap years?
Yes, and it assumes birthdays are equally likely, which is close enough.
How many people for 99%?
About 57.
What formula does the Birthday Paradox Calculator use?
P(shared) = 1 − 365! ÷ ((365 − n)! × 365ⁿ).
Can I work backwards from the result?
Yes. Type the result you want into Chance of a shared birthday and the calculator finds the matching number of people.