THE FEUTEX TOOLKIT

Birthday Collision Estimate

Estimate collision probability and expected matching pairs for independent draws from equal-probability categories.

Probability workspace● Runs in your browser

01 Your input

Independent drawsitemsEqually likely categoriescategories

02 Your result

View or copy raw result data

Result data

FormulaCollision Approx = -expm1(-n*(n-1)/(2*m)); Expected Matching Pairs = n*(n-1)/(2*m)

Sources and model references

https://mathworld.wolfram.com/BirthdayProblem.html

Worked example

Inputs

Independent draws: 23 items
Equally likely categories: 365 categories

Expected results

Collision Approx: 0.5000017522 probability
Expected Matching Pairs: 0.6931506849 pairs

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

Enter the labeled inputs using consistent units.
Check the stated assumptions and calculate.
Review each output and compare another input scenario.

Try this example

{
  "n": 23,
  "m": 365
}

Accuracy and scope

Poisson approximation to at-least-one collision; best when draws are small relative to categories. Expected matching pairs is exact. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.