52 people ≈ 97%
Double the “23 people” headline and you’re nearly guaranteed: 52 people is about a 97% chance of a shared birthday.
Quick math
Birthday Paradox Calculator — Probability of Shared Birthdays
Inputs
Tip: 23 people ≈ 50% chance with 365-day assumption.
This assumes birthdays are uniformly distributed across the chosen number of days.
Results
Set a group size and press Calculate.
Smallest Group for Common Thresholds
| Target Probability | Smallest Group Size |
|---|---|
| ≥ 50% | — |
| ≥ 75% | — |
| ≥ 90% | — |
| ≥ 99% | — |
Outputs are rounded for readability. Exact computations use high-precision log products to avoid underflow.
How the Birthday Paradox Calculator Works
The tool computes the chance that in a group of n people, at least two share a birthday. Under a
uniform model with D possible birthdays (365 by default), the probability of no shared birthdays is
P(no match) = ∏k=0n−1 (D−k) / D. Therefore
P(≥1 match) = 1 − P(no match). We calculate the product in log space for numerical stability.
The famous result is that with just 23 people the chance is about 50% (assuming 365 equally likely birthdays). You can switch to a 366-day model to include 29 February.
Birthday Paradox: FAQs
Why is it called a paradox?
Because the result feels surprising: our intuition often confuses the question “someone matches someone” with “someone matches me.” The calculator answers the former.
Does it assume birthdays are equally likely?
Yes. Real-world data varies by month and region, but the uniform assumption is standard for the paradox and keeps the math transparent.
What if the group size exceeds the number of days?
If n > D, then by the pigeonhole principle the probability is 100%.
Is my data private?
Yes. All calculations run locally in your browser; no data is uploaded or stored on a server.
5 Fun Facts about the Birthday Paradox
Months aren’t equal
September birthdays often dominate in real data, so real-world odds can be slightly higher than the uniform 365-day model suggests.
Real-world skew
Poker paradox cousin
The same math explains why pair collisions in hash functions happen sooner than intuition says—just like matching birthdays in a crowd.
Crypto parallel
Leap day barely moves it
Including 29 February nudges the 50% threshold from 23 to 24 people—a tiny shift despite the extra day.
Leap tweak
Three-way matches
The chance of at least three people sharing a birthday passes 50% around 88 people (365-day assumption).
Higher collisions