Birthday Paradox Calculator
How many people do you need before two probably share a birthday?
Your numbers
Your results
Probability at least two share
Probability at least two share
Probability all different
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Number of pairs
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Birthday Paradox Calculator by TheCalcTools
How the Birthday Paradox Calculator works
Enter the group size.
The calculator finds the chance that everyone has a different birthday.
It subtracts that from 1 to give the chance of at least one match.
The formula
P(all different) = 365! ÷ ((365 − n)! 365ⁿ)P(match) = 1 − P(all different)
Worked example
Using the default values shown in the calculator:
| Number of people | 23 |
|---|
- With 23 people there are 253 pairs.
- P(all different) = 49.27%.
- So the probability of at least one shared birthday is 50.73%.
Result:
| Probability at least two share | 50.73% |
|---|---|
| Probability all different | 49.27% |
| Number of pairs | 253 |
Frequently asked questions
Why is the answer surprisingly high?
Because the number of pairs grows quickly. 23 people form 253 pairs, and each pair has a small chance of matching.
Does it include 29 February?
No. It assumes 365 equally likely birthdays, which is a standard simplification.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.