Birthday Paradox Calculator — Probability of Shared Birthdays
Inputs
Results
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.