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The Excel NORM.INV Function

Related Functions:
NORM.DIST
NORM.S.INV
Normal Distribution

The Normal distribution is a continuous probability function that is given by the formula:

Normal Probability Density Function

where μ is the mean of the distribution, σ2 is the variance, and x is the independent variable for which you want to evaluate the function.

The Cumulative Normal Distribution function is given by the integral, from -∞ to x, of the Normal Probability Density function.

Further information on the Normal Distribution is provided on the Wikipedia Normal Distribution Page.

Function Description

The Excel NORM.INV function calculates the inverse of the Cumulative Normal Distribution Function for a supplied value of x, and a supplied distribution mean & standard deviation.

The Norm.Inv function is new in Excel 2010 and so is not available in earlier versions of Excel. However, the function is simply an updated version of the Norminv function, which is available in earlier versions of Excel.

The syntax of the Norm.Inv function is:

NORM.INV( probability, mean, standard_dev )

Where the function arguments are:

probability - The value at which you want to evaluate the inverse function.
mean - The arithmetic mean of the distribution.
standard_dev - The standard deviation of the distribution.

Excel uses an iterative method to calculate the Norm.Inv function and seeks to find a result, x, such that:

NORM.DIST( x, mean, standard_dev, TRUE ) = probability


Norm.Inv Function Example

Plot of Inverse Normal Cumulative Distribution Function with Mean=5 and Standard Deviation=2
Inverse Normal Cumulative Distribution with mean = 5 & std. dev. = 2

The above chart on the right shows the Inverse Normal Cumulative Distribution Function with a Mean of 5 and a Standard Deviation of 2.

If you want to calculate the value of this function when the probability = 0.6, this can be done using the Excel Norm.Inv function, as follows:

=NORM.INV( 0.6, 5, 2 )

This gives the result 5.506694206.


For further information and examples of the Excel Norm.Inv function, see the Microsoft Office website.


Norm.Inv Function Errors

If you get an error from your Excel Norm.Inv function this is likely to be one of the following:

Common Errors
#NUM! -

Occurs if either:

  • the supplied probability argument is < 0 or > 1
or
  • the supplied standard_dev argument is ≤ 0.
#VALUE! - Occurs if any of the supplied arguments is non-numeric.
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