Weibull distribution calculator
Calculate probabilities and quantiles for a positive lifetime with shape k and scale λ.
How to use this page
- Choose density, CDF, survival or quantile.
- Enter positive k and λ.
- Provide x or probability q and read the result.
What this page does not do: Interpreting k as a failure pattern requires time-to-event data and treatment of censoring. This calculator evaluates a distribution; it does not fit parameters to data.
Further reading
The Weibull distribution is used for positive lifetimes and reliability analysis. Scale λ stretches the time axis, while shape k changes the hazard pattern.
At k=1 Weibull reduces to the exponential distribution. In this model k<1 gives decreasing hazard and k>1 increasing hazard.
Frequently asked questions
What does λ mean?
At x=λ the CDF is 1−e⁻¹, about 63.2%, regardless of k.
Does this calculator estimate parameters?
No. It evaluates supplied parameters; estimation requires a separate fitting procedure.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).