Calculadora do Paradoxo do Aniversário
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P = 1 − ∏ (365 − k) / 365 de k=0 a n−1
About this calculator
The Birthday Paradox Calculator determines the probability that, in a group of n people, at least two share the same birthday. The paradox shows that this probability is surprisingly high even for small groups. For example, with 23 people, the chance exceeds 50%; with 70 people, it surpasses 99.9%.
The calculation uses the formula P = 1 − ∏ (365 − k)/365, where k ranges from 0 to n−1. We multiply the probabilities of each person not matching any previous one and subtract the result from 1. This assumes birthdays are independent and uniformly distributed over the year, ignoring leap years.
Use this calculator for event planning, probability studies, or mathematical curiosity. For instance, you can estimate the chance that two coworkers or students share a birthday. It is an educational tool to understand combinatorial probability concepts.
Caveats: the calculator assumes 365 days per year, disregarding February 29. For real groups, the probability may slightly differ if birth seasonality exists. Also, the paradox refers to any pair, not a specific date. Do not confuse with the probability of someone having a birthday on a given date.
Frequently asked questions
Why is the probability already above 50% with 23 people?
Because the number of possible pairs grows quickly. With 23 people, there are 253 pairs, and the chance of no pair matching decreases rapidly.
Does the calculator consider leap years?
No. It uses 365 days. To include February 29, a more complex model would be needed, but the impact is small.
What is the probability that someone shares a birthday with me?
That is different. The chance of a specific person having the same birthday as you is 1/365 (about 0.27%). The calculator deals with any coincidence in the group.
Can I use this calculator to plan a raffle?
Yes, if you want to avoid two people winning on the same day. But remember the paradox applies to any coincidence, not a pre-defined date.