How to use the WEIBULL.DIST function in Excel

In this article, we will learn How to use the WEIBULL.DIST function in Excel.

What is Weibull distribution?

The Weibull distribution is a two-parameter family of continuous probability distributions. It is named after Swedish mathematician Waloddi Weibull. This type of distribution is generally used for the distribution in reliability analysis or the analysis of time to failure. For example finding the mean time of medical and dental implants or Components produced in a factory (like bearings, capacitors, or dielectrics) or warranty analysis for a product. The function depends on the two parameters lambda and k. Now let's see how the parameters affect the probability factor. Gamma distribution(CDF) can be carried out in two types one is cumulative distribution function, the mathematical representation and weibull plot is given below.

You can see the effect of changing parameters with different color lines as indicated in the plot with the mathematical formula stated below it.

Now we proceed to the other part which is probability density function which is extracted when you differentiate the above equation. We get the probability mass distribution plot and mathematical formula stated below.

when plotted on graph having given parameters lambda  and k.

The gamma distribution plot is shown above. As you can see these are complex functions to extract probability using it in excel. So excel provides the inbuilt statistical function to get weibull distribution function results. Let's understand how to use the WEIBULL.DIST function to work as an weibull distribution calculator.

WEIBULL.DIST Function in Excel

WEIBULL.DIST is a statistical function which returns the weibull distribution at a particular value. It takes the value and the two parameters named alpha and beta along with the type of distribution required(cdf or pdf). Let's understand these arguments with the function syntax as explained below.

WEIBULL.DIST Function syntax :

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

x : value at which you want to evaluate the distribution.

alpha : parameter for the weibull distribution. If alpha = 1, WEIBULL.DIST acts as the exponential distribution function.

beta : parameter for the weibull distribution.

cumulative : logical value that determines the form of the function. If cumulative is TRUE, WEIBULL.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.


Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have the x value along with alpha and beta parameters for the weibull distribution stated below.

Now using these parameters, we will evaluate the cumulative distribution for the weibull function with the formula stated below.

Use the formula:


As you can see, the formula returns the cumulative probability value exactly at 105 comes out to be 0.036 or 3.6%.

Now to calculate the value for at least 105 we can use the probability mass distribution formula by changing the cumulative argument. Use the formula to find the probability for weibull distribution given the same parameters. 

Use the formula:


As you can see, the formula returns the cumulative probability value  for at least 105 comes out to be 0.930 or 93%.  

Here are all the observational notes using the WEIBULL.DIST function in Excel
Notes :

  1. The function only works with numbers. If any argument other than cumulative is non numeric, the function returns #VALUE! error.
  2. The function returns #NUM! Error.
    1. If x < 0
    2. If alpha < =0
    3. If beta < = 0
  3. The cumulative argument can be used with boolean numbers (0 and 1) or (FALSE or TRUE).
  4. You can feed the arguments to the function directly or using the cell reference as explained in the example.

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