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Cauchy Distribution Calculator

Find cumulative probability for a Cauchy distribution from location and scale.

Data stays on this deviceConvention explained below
Probability workspace
Probability workspace

Probabilities range from 0 to 1. Check whether the method gives cumulative or exact-count probability.

See the method

Set model parameters

Runs on your device

Your probability

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter location, scale, value x.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

CDF = 1/2 + atan((x−location)/scale)/π.

A WORKED EXAMPLE

Using location = 0, scale = 1, value x = 1, the result is 0.75. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Location is the median, not an expected value. A Cauchy distribution has no finite mean or variance.

What to keep in mind

Location is the median, not an expected value. A Cauchy distribution has no finite mean or variance. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

How do I use this cauchy distribution calculator?

Find cumulative probability for a Cauchy distribution from location and scale. Enter location, scale, value x. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Location is the median, not an expected value. A Cauchy distribution has no finite mean or variance.

Methodology maintained by ClarityKit. How these tools are built and checked.