Calculate the surprising probability that two people in a group share the same birthday.
Group Settings
participants
Lone Soul50% Mark (23)Near Certainty (70+)
Even a small group of 23 people has a >50% chance of a birthday match!
Probability Analysis
Match Probability50.73%Statistically Likely
Possible Pairs253nC2 combinations
Uniqueness Prob.49.27%
EffectHigh
Crowd Density23
You've crossed the 50% threshold where shared birthdays become likely!
About this calculator
Overview
The birthday paradox, also known as the birthday problem, is a counter-intuitive observation in probability theory that in a randomly chosen group of 23 people, there is a more than 50% chance that at least two people will have the same birthday.
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Pro Tips
The probability grows much faster than the number of people because the number of possible *pairs* grows quadratically.
The exact formula is 1 - [365! / (365ⁿ * (365-n)!)].
You only need 23 people to reach the 'break even' 50% probability mark.
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Fun Facts
"With 70 people, the probability of a shared birthday is a staggering 99.9%."
"The paradox arises because our brains tend to think about matching *one* specific person's birthday, rather than *any* two people in the room."
"In a group of 23, there are 253 separate pairs of people who could potentially share a birthday."
