Rayleigh Distribution Calculator

Your details

Choose what to compute: density and cumulative probability at a point, the x-value for a given probability, or the full set of statistical measures.
The scale parameter sigma (sigma > 0) stretches or compresses the distribution. Larger sigma shifts the peak and spreads the distribution wider.
The non-negative value at which to evaluate the PDF and CDF.
Probability Density f(x)
0.303265

Height of the density curve at the given x

Cumulative Probability F(x)0.393469
Mean2.506628
Median2.35482
Mode2
Variance1.716815
Standard Deviation1.310273
Skewness0.631111
0.3032654.5% below · x

Rayleigh distribution with sigma = 2

  • With sigma = 2, the average value is 2.5066, the median is 2.3548, and the peak density (mode) is exactly 2.
  • The standard deviation is 1.3103. About 63.2% of values fall at or below the mean, reflecting the right-skewed shape.
  • At x = 2: the density is 0.303265 and the cumulative probability is 39.35%, meaning 39.35% of outcomes fall at or below this value.
  • The Rayleigh distribution arises naturally when a two-dimensional vector has independent, identically distributed normal components: its magnitude follows a Rayleigh distribution.

Next stepAdjust sigma to see how the distribution stretches. Larger sigma increases both the mean and spread proportionally.

 = Powered by OnlyCalculators