Birthday Paradox Calculator
Find the probability of shared birthdays in a group.
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Enter the number of people in the group and the number of days in a year (365 by default). The calculator computes the probability that at least two people share a birthday. The classic result: with just 23 people, there is a 50.7% chance.
About This Calculator
The birthday paradox is a famous probability result that surprises most people. It shows that in a group of just 23 people, there is a greater than 50% chance that two share a birthday. With 70 people, it exceeds 99.9%. The math works because you are comparing all possible pairs, not just comparing one person to everyone else.
Frequently Asked Questions
Why is it called a paradox?
It is not a true paradox, just counterintuitive. People expect you need close to 365 people, but 23 is enough for a 50% chance because there are 253 possible pairs to compare.
How many people for a 99% probability?
You need about 57 people for a 99% probability of at least one shared birthday.
Does this assume uniform birthday distribution?
Yes. Real birthdays are not uniformly distributed (more births in some months), which actually makes the probability slightly higher than this calculation.