Birthday Problem Calculator

Number of people

Treat year as leap year (366 days)

Off = 365 days (ignore Feb 29), On = 366 days (include Feb 29).

Discover the likelihood that two individuals in a group have the same birthday using our Birthday Problem Calculator. Dive into the well-known paradox, grasp the underlying formula, and quickly compute results for any group size.

What Is the Birthday Problem (Birthday Paradox)

The Birthday Problem asks a simple question:

“In a group of n people, what is the probability that at least two of them share the same birthday?”

Mathematically, the probability increases to 50% at just 23 people and to 99% at 57 people.

How Is the Birthday Problem Calculated?

Step 1 – Find the probability that no one shares a birthday.

For n people:

Formula for No-Match Probability

P (no shared birthday) = \frac{365}{365} \times \frac{364}{365} \times \frac{363}{365} \times \dots \times \frac{365 - n + 1}{365}

Assuming 365 in a year.

Step 2 – Subtract from 1

P (at least one shared birthday) = 1 - P (no shared birthday)

This gives the final probability that at least two people in the group share a birthday.

How to Use Our Birthday Problem Calculator?

Enter the no. of people in a group.
“Check” if you wish to calculate the probability for a leap year.
Click “Calculate” and the calculator computes the probability.

Birthday Problem Calculator