Birthday Paradox Visualizer
Find the smallest group size where the chance of a shared birthday crosses any threshold you choose. Includes a heatmap and a "what's the chance in my classroom?" helper.
Setup
Advertisement
Result
Heatmap (group size vs. collision probability)
Curve
Why "paradox" is a misnomer
It's not actually a paradox — it's a counter-intuitive counting problem. With N people, there are C(N,2) = N(N-1)/2 pairs of people. For N=23 there are 253 pairs, each with probability 1/365 of sharing a birthday. So the expected number of matching pairs is 253/365 ≈ 0.69 — and the probability of at least one pair matching is 50.7%.
This matters in practice for hash collisions in cryptography, deduplication, and birthday attacks on digital signatures.
Who uses it
- Educators teaching pigeonhole / combinatorial reasoning.
- Software engineers sizing hash tables to avoid collisions.
- Anyone who's lost a bet about a classroom of 30 students.
Limitations
- Assumes uniform birthday distribution. Real births cluster in late summer/fall in northern-hemisphere countries.
- Assumes independence (no twins). Twin pairs hit roughly 1 in 333 births, negligible for small N.
- Does not compute probability of exactly one shared birthday, only "at least one collision".