Comprehensive Calculator Guide
This calculator gives the chance that at least two people in a group share a birthday. Just 23 people pass 50% (50.73%); 70 reach 99.9%. It also shows the number of pairs and works for any number of possible days.
Why it surprises
The question is about any pair, and 23 people make 253 pairs. Work via the complement: 1 − (365/365)(364/365)… The same maths sets the length of digital fingerprints.
How to Use
- Enter the group size.
- Keep 365 days or change it.
- Press “Calculate” to see the chance.
Formula Used
P = 1 − 365!/((365 − n)! 365^n) | Pairs = n(n − 1)/2
Practical Examples
- Example 1
- 23 people: 50.73%.
- Example 2
- A class of 30: 70.63%.
Important Tips
- Try it with 30+ people.
- Change the days for similar problems.
- It’s any pair, not you.
Common Mistakes to Avoid
- Dividing n by 365.
- Confusing it with sharing your birthday.
- Forgetting equal-day assumption.
Frequently Asked Questions
- People for 50%?
- 23.
- For certainty?
- 366.
- Someone sharing mine among 23?
- About 5.9%.