Why this tool is useful
Understand collision risk in classrooms, teams, identifiers and hash-like spaces without sending a participant list anywhere.
Everyday Calculators · runs locally
Birthday Paradox Probability Calculator
Estimate the probability that at least two people share a birthday using the standard exponential approximation.
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How it works
It applies 1 - exp(-n(n-1)/(2d)), where n is the group size and d is the number of equally likely possible dates.
Practical example
For 23 people and 365 equally likely birthdays, the approximation is close to the familiar one-half threshold.
Validation
The calculation is deterministic and explains validation errors instead of silently changing invalid input.
Privacy boundary
Input and output remain in this tab. Copy and download happen through browser APIs without a server upload.
Result passport
Every run reports its tool mode, timestamp and input/output size so transformed data can be audited.