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Birthday Paradox Calculator
See the exact chance that two people in a group share a birthday.
Shared birthday probability
Chance of a shared birthday: —
Chance all birthdays differ: —
People needed for 50 percent: —
How to use the Birthday Paradox Calculator
- Enter the number of people in the group.
- Choose how many group sizes you want listed in the table.
- Read the exact shared birthday chance and the row where it passes fifty percent.
Features
- Exact complement formula, not an approximation
- Probability table across a range of group sizes
- Highlights the first size to pass fifty percent
- Runs locally, no uploads
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Frequently Asked Questions
Common questions about the free online birthday paradox calculator.
It is the surprising result that a group of only twenty-three people already has a better
than even chance of two of them sharing a birthday.
The tool multiplies one minus each fraction from one over 365 up to n minus one over 365,
then takes the complement of that product.
The complement product is the true probability, while shortcuts assume draws are independent
and drift away from the correct value for larger groups.
Twenty-three people give about 50.7 percent, which is the point where a shared birthday
becomes more likely than not.
The probability is above 99.9 percent, so in a group of seventy people a shared birthday is
almost certain.
No. The calculation uses 365 equally likely days, which matches the standard statement of the
problem.
Not perfectly, because real birth data has seasonal peaks, and that uneven spread makes a
shared birthday slightly more likely still.
No. It is a probability, so a group of twenty-three people still has about a forty-nine
percent chance that every birthday is different.
No. The probability is computed in your browser and nothing you type is ever sent to a
server.
Yes. It is completely free, needs no account and places no limit on how many group sizes you
test.
Last updated: October 10, 2026