The NORM.DIST function is a Statistical formula that calculates and returns the normal distribution of a value for the specified mean (average) and standard deviation. The NORM.DIST function can calculate either the Normal Probability Density Function or the Cumulative Normal Distribution Function. In this guide, we’re going to show you how to use the NORM.DIST (NORM DIST) function and also go over some tips and error handling methods.


Supported versions

  • Excel 2010 and later

Excel NORM.DIST Function Syntax

NORM.DIST(x,mean,standard_dev,cumulative)


Arguments

xThe value for which you want the distribution.
meanThe arithmetic mean of the distribution.
standard_devThe standard deviation of the distribution.
cumulative

A logical value which specifies the type of the distribution.

  • FALSE = Probability density function
  • TRUE = Cumulative distribution function

NORM.DIST Function Use Cases

Probability density function

The NORM.DIST function uses the probability density function when cumulative argument is set to FALSE logical value. The equation for the normal density function is  where x is the value, μ is the mean and σ is the standard deviation. Enter the mean and standard deviation values into the function to calculate. For example, the normal density function returns 0.34 for value 23, with a mean of 26.44 and standard deviation of 11.17.

=NORM.DIST(23,26.44,11.17,FALSE)

If your place the calculated return numbers on a chart, set you will get a bell curve.

norm.dist

Cumulative normal distribution function

The other mode of the NORM.DIST function is the cumulative normal distribution. The cumulative distribution function uses the integral from negative infinity to x of the probability density function. Set the cumulative argument to TRUE logical value to evaluate the cumulative distribution. The other arguments work the same as in the previous example.

=NORM.DIST(23,26.44,11.17,FALSE)

If you create a graph from the results of the cumulative normal distribution function, you will get something similar to the following.

norm.dist

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Tips

  • You can use the STDEV.P or STDEV.S functions to calculate the standard deviation for the entire population or a sample respectfully.
  • You can use the AVERAGE function to calculate the mean of a data set.
  • The NORMDIST is the older version of this function. We recommend refraining from using the NORMDIST function.
  • Similar functions:
    • NORM.INV function returns the inverse of the cumulative distribution.
    • NORM.S.DIST function returns the standard distribution.
    • NORM.S.INV function returns the inverse of the standard cumulative distribution.

Issues

  • The NORM.DIST (NORM DIST) function returns #NUM! error value if the standard_dev argument is ≤ 0.