NORM.DIST function

Returns the normal distribution for the specified mean and standard deviation. This function has a very wide range of applications in statistics, including hypothesis testing.



The NORM.DIST function syntax has the following arguments:

  • X     Required. The value for which you want the distribution.

  • Mean     Required. The arithmetic mean of the distribution.

  • Standard_dev     Required. The standard deviation of the distribution.

  • Cumulative     Required. A logical value that determines the form of the function. If cumulative is TRUE, NORM.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.


  • If mean or standard_dev is nonnumeric, NORM.DIST returns the #VALUE! error value.

  • If standard_dev ≤ 0, NORM.DIST returns the #NUM! error value.

  • If mean = 0, standard_dev = 1, and cumulative = TRUE, NORM.DIST returns the standard normal distribution, NORM.S.DIST.

  • The equation for the normal density function (cumulative = FALSE) is:


  • When cumulative = TRUE, the formula is the integral from negative infinity to x of the given formula.


Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.




Value for which you want the distribution


Arithmetic mean of the distribution


Standard deviation of the distribution





Cumulative distribution function for the terms above



Probability mass function for the terms above


Applies To: Excel 2016 for Mac, Excel 2016, Excel Starter, Excel 2010, Excel Online, Excel 2013, Excel for Mac 2011

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