๐ Birthday Paradox Simulator
50.7%
Probability at least two people share a birthday
Enter a group size to calculate the probability that at least two people in that group share the same birthday (month and day). A hands-on way to explore the famously counter-intuitive "birthday paradox."
How to use
- Use the slider to set the group size.
- Adjust the number of days in a year if needed (normally 365).
- The probability that at least two people share a birthday is calculated automatically.
FAQ
What is the "birthday paradox"?
The counter-intuitive mathematical fact that in a group of just 23 people, there's already more than a 50% chance that two of them share a birthday. It's called a paradox because most people intuitively expect it would take far more people, given there are 365 possible days.
What formula does this use?
It calculates the probability that everyone has a *different* birthday, then subtracts that from 1 to get the probability that at least two share one. The "all different" probability is computed by multiplying 365/365 ร 364/365 ร 363/365 ร ... once for each person.
Does this account for leap years (February 29 birthdays)?
No, for simplicity it assumes a fixed year length (365 by default). You can change the "days in a year" field to model other cases, such as including leap days or considering only birth months (12).