Birthday Paradox Simulator

Calculate exact shared-birthday probability and watch repeated classes converge.

Default assumes equally likely birthdays and ignores leap day.

Exact probability

Ready

At least one shared birthday.

Simulated probability
Not run
Pairs compared
253
Trials completed
Not run

The pair count grows as n(n - 1) / 2.

Run the simulation to fill Monte Carlo metrics and convergence.

Convergence checkpoints
TrialMatching trialsSimulated probability
Export

P(match) = 1 - product((days - i) / days), i = 0..people - 1 How?

How this is calculated

The exact calculation multiplies the probability that each new person has a birthday not already seen, then takes the complement. The simulation assigns random day numbers and records whether any birthday repeats.

Formula: P(match) = 1 - product((days - i) / days), i = 0..people - 1

Sources

  1. Wolfram MathWorld Birthday Problem. Wolfram MathWorld. Retrieved .

Method last reviewed