Probability Someone Shares Your Birthday

Find the chance that someone among n people shares your exact birthday. Using 1 minus (364/365) to the power n, see the match chance, the no-match chance, and how many people pass 50 percent.

Input

How many people do you need before someone shares your birthday? Enter a group size to see the probability.

Number of people (besides you)

people

Result

Chance someone among 253 people shares your birthday

50.05%

Chance no one matches

49.95 %

People needed to pass 50%

253 people

Formula

No-match chance = (364 / 365) to the power of 253

Match chance = 100% minus 49.95% = 50.05%

How it works

We fix your own birthday and treat each of the other n people as having a 1/365 chance of sharing it. Leap years and seasonal birth patterns are ignored in this simplified model.
The chance that all n people have a birthday different from yours is (364/365) raised to the power n. This is the no-match probability.
The chance that at least one person shares your birthday is 1 minus the no-match probability.
You need 253 people for the match probability to pass 50 percent. This equals ln(0.5) divided by ln(364/365), rounded up.
This is a different question from the birthday paradox, which asks whether any pair among n people shares a birthday. The paradox compares all pairs, so it passes 50 percent at just 23 people. This calculator fixes the reference to you alone, so the probability is much smaller for the same group size.

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