Birthday Paradox Calculator
The surprising result is that a small group is as likely as not to contain a shared birthday.
At least two share a birthday
—
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
Everyone’s is different —
Someone shares yours —
Smallest group for an even chance —
Reading this —
The formula
P(all different) = (d − 1)/d × (d − 2)/d × … × (d − n + 1)/d P(a match) = 1 − P(all different)
The product is added up as logarithms, so large groups stay accurate.
What to watch out for
It feels wrong because we think about a match with ourselves. But any pair counts, and 23 people make 253 pairs.
Frequently Asked Questions
How many people for a 50% chance?
23, where the chance is 50.73%.
And with 70 people?
99.92%.
How many to share my birthday, specifically?
Far more: 253 other people for an even chance.