Weibull Distribution Calculator

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Choose whether to evaluate the distribution at a point x, invert the CDF, or calculate a range probability.
The scale parameter controls the spread of the distribution. Must be > 0.
k < 1: decreasing hazard (infant-mortality failures). k = 1: constant hazard (exponential). k = 2: Rayleigh. k > 1: increasing hazard (wear-out failures). k = 3.4 approximates the normal distribution.
The point at which to evaluate the PDF, CDF, survival function, and hazard rate.
PDF f(x)
0.735759

Probability density at x

CDF F(x)0.632121
Survival S(x)0.367879
Hazard rate h(x)2
Mean0.886227
Median0.832555
Mode0.707107
Variance0.214602
Std deviation0.463251
Mean0.886227
Median0.832555
Std deviation0.463251

Weibull distribution with scale 1, shape 2.00: evaluated at x = 1

  • With k approximately 2, this is the Rayleigh distribution, often used to model wind speed and certain signal amplitudes.
  • The mean is 0.8862 and the standard deviation is 0.4633.
  • At x = 1, there is a 63.21% chance the variable is at or below this value, and a 36.79% survival probability.
  • The coefficient of variation is 52.3% (std dev / mean), indicating moderate relative variability.

Next stepFor reliability analysis, the survival function S(x) gives the probability of surviving past time x, while the hazard rate h(x) quantifies the instantaneous risk of failure.

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