Statistics & Probability

Instant, private, and free

Birthday Paradox Calculator.

Find the chance that at least two people share a birthday.

On-device calculationNo signup
01

Set your values

Results update as you type.

collisionProbability: 0.507297

collisionProbability

0.507297
noCollisionProbability: 0.492703

noCollisionProbability

0.492703

Results update automatically as you type.

Use Cases

Event Planning and Icebreakers

Use the calculator to find the group size where shared birthdays become likely, making for a fun party trick or to plan birthday-themed events.

Example: For a party of 30 people, the probability of a shared birthday is about 70%.

Educational Demonstrations

Teachers and students can explore probability concepts by adjusting group size and possible birthdays to see how quickly the probability rises.

Example: Show that with 50 people, the chance exceeds 97%.

Frequently Asked Questions

What is the Birthday Paradox?
The Birthday Paradox is the surprising result that in a group of just 23 people, there's about a 50% chance that two people share a birthday. It's not a logical paradox but a counterintuitive probability fact.
How does the calculator compute the probability?
The calculator uses the formula: 1 - (possible birthdays! / ((possible birthdays - people)! * possible birthdays^people)). It assumes each birthday is equally likely and ignores leap years unless you set possible birthdays to 366.
What if I change the number of possible birthdays?
You can adjust the 'Possible birthdays' field to model different scenarios, such as 365 for a standard year, 366 for leap years, or other values for custom situations. This changes the probability accordingly.

Tips & Common Mistakes

Tips

  • For a standard year, keep 'Possible birthdays' at 365. For leap years, use 366.
  • The probability increases rapidly with group size; even small groups can have surprisingly high chances.
  • Use the calculator to find the minimum group size needed to reach a desired probability, like 50% or 90%.
  • Remember that the calculation assumes birthdays are uniformly distributed; real-world data may vary slightly.

Common Mistakes to Avoid

  • Forgetting to adjust 'Possible birthdays' for leap years, which can slightly alter the probability.
  • Assuming the probability is the chance that a specific person shares a birthday, rather than any two people in the group.
  • Using the calculator for groups larger than the number of possible birthdays, which results in a 100% probability (since the pigeonhole principle applies).

Last updated: August 13, 2026