Calculate any-pair birthday collision probability and the minimum group size for a target, with adjustable uniform bucket count.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs. Probability inputs are percentages from 0 to 100, not decimal fractions.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
P(at least one shared birthday) = 1 − ∏(1−i/d), for i = 0,…,n−1.
Assumptions and limits
Independent uniform draws into d buckets; leap days and seasonal birthday variation are not modeled. Any-pair collision differs from matching one named birthday.
Worked example
With 23 people and 365 equally likely birthdays, the probability that at least two share a day is about 50.7297%. The minimum group size reaching 50% is therefore 23. There are 253 distinct pairs in that group. This is not the probability that someone matches one specified birthday; that narrower event uses another formula. Bucket count can represent a small uniform identifier space as well as days.
Worked reading and practical questions
- A Shared Birthday vs Your Birthday: Two Different Questions
- Birthday Collisions in Small Random Identifier Spaces
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Independent uniform draws into d buckets; leap days and seasonal birthday variation are not modeled. Any-pair collision differs from matching one named birthday.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.