Weibull Distribution Calculator

Work out weibull distribution instantly with clear inputs, formula shown and shareable results.

About Weibull Distribution Calculator

The Weibull distribution is the workhorse of reliability engineering. Its shape parameter controls the failure pattern: k < 1 gives decreasing hazard (infant mortality), k = 1 constant hazard, and k > 1 wear-out.

Formulas

Weibull CDF

F(x) = 1 − exp(−(x/λ)ᵏ)

Mean life

E = λ·Γ(1 + 1/k)

Worked example

With the default values below, Weibull Distribution Calculator returns P(failure by x) of 0.4727075760. Change any input above and every figure here is recalculated in your browser.

Inputs used

Shape kminimum 0: 2
Scale λminimum 0: 100
Evaluate at xminimum 0: 80

Results

P(failure by x): 0.4727075760
Reliability R(x): 0.5272924240
Mean life λ·Γ(1 + 1/k): 88.622693
Instantaneous hazard rate: 0.0160000000

Step by step

1Values used
2Weibull CDF
3Mean life
4P(failure by x)= 0.4727075760
5Reliability R(x)= 0.5272924240
6Mean life λ·Γ(1 + 1/k)= 88.622693
7Instantaneous hazard rate= 0.0160000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For k = 2, λ = 100 at x = 80?

F = 1 − e^(−0.64) ≈ 0.4727, so reliability is about 52.7% and the mean life is 100·Γ(1.5) ≈ 88.62.

What does k = 1 mean?

The Weibull reduces to the exponential distribution with a constant hazard rate — failures are memoryless.