Weibull Distribution Calculator

What the Weibull Distribution Models

The Weibull distribution models positive continuous data such as failure times, wind speeds, and material strengths. Its shape parameter controls skewness and tail behavior. Related tools: Exponential Distribution Calculator and Normal Distribution Calculator.

Weibull Formulas

$$F(x) = 1 - e^{-(x/\lambda)^k}, \quad x \ge 0$$

$$f(x) = \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1} e^{-(x/\lambda)^k}$$

$$Q(p) = \lambda[-\ln(1-p)]^{1/k}$$

$$\mu = \lambda \Gamma\left(1 + \frac{1}{k}\right)$$

Example

With scale $\lambda = 10$, shape $k = 2$, and $x = 6$, we get $P(X \le 6) = 1 - e^{-(0.6)^2} \approx 0.3025$.