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WEIBULL.DIST Function

Excel 2010+, Excel 2013, Excel 2016, Excel 2019, Excel 365

Summary

The WEIBULL.DIST function calculates the Weibull probability distribution, essential for reliability engineering and life data analysis. It models failure rates and time-to-failure scenarios for products and systems.

Syntax

WEIBULL.DIST(x, alpha, beta, cumulative)

Parameters

Parameter	Type	Required	Description
x	`Number`	Yes	Value at which to evaluate the distribution (must be ≥ 0)
alpha	`Number`	Yes	Shape parameter of the Weibull distribution (must be > 0)
beta	`Number`	Yes	Scale parameter of the Weibull distribution (must be > 0)
cumulative	`Boolean`	Yes	TRUE for cumulative distribution function (CDF), FALSE for probability density function (PDF)

Using the WEIBULL.DIST Function

WEIBULL.DIST is widely used in reliability engineering to model the probability of failures over time. Set cumulative to TRUE for the cumulative distribution (probability of failure by time x) or FALSE for the probability density (failure rate at time x). When alpha=1, it becomes the exponential distribution.

Common WEIBULL.DIST Examples

Cumulative Distribution (CDF)

=WEIBULL.DIST(105,20,100,TRUE)

Probability that device fails before 105 hours: 0.929581 (92.96%)

Probability Density Function (PDF)

=WEIBULL.DIST(105,20,100,FALSE)

Failure rate density at 105 hours: 0.035589

Exponential Distribution Case

=WEIBULL.DIST(50,1,100,TRUE)

Exponential distribution (alpha=1) cumulative probability: ~0.3935

Frequently Asked Questions

TRUE returns the cumulative distribution function (CDF) - probability of failure ≤ x. FALSE returns the probability density function (PDF) - instantaneous failure rate at x.

WEIBULL.DIST is the modern replacement with identical functionality but better syntax clarity.

Yes, when alpha=1, WEIBULL.DIST produces the exponential distribution with constant failure rate.

Common Errors and Solutions

#NUM! error

Cause: x < 0, or alpha ≤ 0, or beta ≤ 0

Solution: Ensure x ≥ 0, alpha > 0, and beta > 0

#VALUE! error

Cause: Non-numeric input for x, alpha, beta, or cumulative

Solution: Use valid numbers for x, alpha, beta and TRUE/FALSE for cumulative

Notes

x represents time/hours/cycles to failure
Alpha (shape) determines if hazard rate increases (α>1), decreases (α<1), or constant (α=1)
Beta (scale) stretches/compresses the distribution
Available since Excel 2010
Replaces WEIBULL function from earlier versions

Compatibility

Available in: Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 365

Not available in: Excel 2007 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+, Excel 2013, Excel 2016, Excel 2019, Excel 365