Search Ctrl K
Home / Tools
THE FEUTEX TOOLKIT

Rayleigh Distribution Profile

Evaluate Rayleigh density, cumulative probability, mean and variance for a nonnegative magnitude.

Probability workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaCdf = -expm1(-(x**2)/(2*s**2)); Density = x/s**2*exp(-(x**2)/(2*s**2)); Mean = s*sqrt(PI/2); Variance = (2-PI/2)*s**2
Sources and model references

Worked example

Inputs

Scale
2 value
Evaluation value
2 value

Expected results

Cdf
0.3934693403 probability
Density
0.3032653299 1/value
Mean
2.506628275 number
Variance
1.716814693 number

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

How to use this tool

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

Try this example

{
  "s": 2,
  "x": 2
}

Accuracy and scope

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.