Birthday Paradox Simulator

Explore the surprising probability of shared birthdays

Quick Facts

23
People needed for 50% probability
50.7%
Probability with 23 people
70
People needed for 99.9% probability
253
Pairwise comparisons with 23 people

Simulation Controls

23 people
1,000 trials

Understanding the Paradox

Why 23 People?

With 23 people, there are 253 pairwise comparisons (23 × 22 / 2).

Each pair has a 1/365 ≈ 0.27% chance of matching birthdays.

Combined, these give approximately 50.7% probability of at least one match!

Common Misconception

People often think: "What's the chance someone shares MY birthday?" (much lower)

The actual question: "What's the chance ANY two people share a birthday?" (much higher)

Key Probabilities

Group Size Probability of Match Number of Pairs
10 11.7% 45
20 41.1% 190
23 50.7% 253
30 70.6% 435
50 97.0% 1,225
70 99.9% 2,415