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Statistics Calculators
Birthday Paradox Calculator
Calculate the probability that at least two people in a group share the same birthday — the classic birthday paradox.
Probability of a shared birthday
Probability of no shared birthday
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About the Birthday Paradox Calculator
The birthday paradox shows that shared birthdays become likely in surprisingly small groups. It's easier to calculate the probability that nobody shares a birthday, then subtract from 1 to find the probability that at least one pair does.
Formula: P(no shared birthday) = (365/365) × (364/365) × (363/365) × ... for n people · P(shared) = 1 − P(no shared)
With just 23 people, there's over a 50% chance two share a birthday — far more than most people's intuition suggests, because the comparison is between every possible pair, not just one person against the rest.
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