The Birthday Paradox shows that in a group of just 23 people, there is a 50% chance that two people share the same birthday. Use the calculator below to find the probability for any group size, or run the simulation to see it in action.
Enter a number between 2 and 365
| People | Probability |
|---|---|
| 5 | 2.71% |
| 10 | 11.69% |
| 15 | 25.29% |
| 20 | 41.14% |
| 23 | 50.73% |
| 25 | 56.87% |
| 30 | 70.63% |
| 40 | 89.12% |
| 50 | 97.04% |
| 60 | 99.41% |
| 70 | 99.92% |
| 75 | 99.97% |
With just 23 people, there is already a 50% chance of a shared birthday. At 70 people, it's virtually certain (99.9%).
The Birthday Paradox demonstrates how our intuition about probability can be misleading. It shows that in a relatively small group of people, the probability of two people sharing a birthday is surprisingly high.
The probability is calculated using the complement rule:
For n people:
Key probabilities:
The Birthday Paradox shows that in a group of just 23 people, there is a 50% chance that two people share the same birthday. Use the calculator below to find the probability for any group size, or run the simulation to see it in action.
Enter a number between 2 and 365
| People | Probability |
|---|---|
| 5 | 2.71% |
| 10 | 11.69% |
| 15 | 25.29% |
| 20 | 41.14% |
| 23 | 50.73% |
| 25 | 56.87% |
| 30 | 70.63% |
| 40 | 89.12% |
| 50 | 97.04% |
| 60 | 99.41% |
| 70 | 99.92% |
| 75 | 99.97% |
With just 23 people, there is already a 50% chance of a shared birthday. At 70 people, it's virtually certain (99.9%).
The Birthday Paradox demonstrates how our intuition about probability can be misleading. It shows that in a relatively small group of people, the probability of two people sharing a birthday is surprisingly high.
The probability is calculated using the complement rule:
For n people:
Key probabilities:
