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Rayleigh Distribution Calculator

Find cumulative probability for a nonnegative Rayleigh-distributed magnitude.

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 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−exp[−x²/(2 scale²)].

A WORKED EXAMPLE

Using scale = 1, value x = 1, the result is 0.39346934. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Scale is the standard deviation of each underlying independent zero-mean normal component, not the standard deviation of the magnitude.

What to keep in mind

Scale is the standard deviation of each underlying independent zero-mean normal component, not the standard deviation of the magnitude. 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 rayleigh distribution calculator?

Find cumulative probability for a nonnegative Rayleigh-distributed magnitude. Enter scale, value x. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Scale is the standard deviation of each underlying independent zero-mean normal component, not the standard deviation of the magnitude.

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