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The NORM.INV function returns the inverse of the cumulative normal distribution for a specified mean and standard deviation. It is commonly used in statistical analysis to find the value at which a specified percentage of observations occur below that value.


Use the NORM.INV formula with the syntax shown below, it has 3 required parameters:

=NORM.INV(x, mean, standard_deviation)
  1. x (required):
    The probability of the value occurring below the mean.
  2. mean (required):
    The arithmetic mean of the distribution.
  3. standard_deviation (required):
    The standard deviation of the distribution.


Here are a few example use cases that explain how to use the NORM.INV formula in Google Sheets.

Finding the z-score for a given probability

Suppose we want to find the z-score for which there is a 25% chance of getting a value lower than that. We can use NORM.INV with x = 0.25, mean = 0 and standard_deviation = 1 to find this value.

Generating a random sample from a normal distribution

We can use the RAND function along with NORM.INV to generate a random sample from a normal distribution with a given mean and standard deviation. Setting x = RAND(), mean and standard_deviation as desired, we can generate a random number that follows a normal distribution.

Calculating confidence intervals

Suppose we have a dataset with a normal distribution and we want to calculate a confidence interval for the mean. We can use NORM.INV along with other functions such as AVERAGE, STDEV.S and COUNT to calculate the confidence interval for a specified confidence level.

Common Mistakes

NORM.INV not working? Here are some common mistakes people make when using the NORM.INV Google Sheets Formula:

Incorrect arguments

One of the arguments provided is incorrect or in the wrong order. Double-check the syntax and ensure that the arguments are entered in the correct order.

Invalid mean or standard deviation

The mean or standard deviation provided is invalid (e.g. negative). Ensure that the mean and standard deviation are valid values.

Non-numeric input

The input provided for x, mean, or standard_deviation is not a number. Check that the input is numeric and formatted correctly.

The following functions are similar to NORM.INV or are often used with it in a formula:


    The NORM.S.INV function is a statistical function in Google Sheets that returns the inverse of the standard normal cumulative distribution function for a specified value. In other words, it returns the z-score that corresponds to a given probability. This function is commonly used in hypothesis testing, confidence interval estimation, and other statistical analyses.


    The NORM.DIST formula is a statistical function that returns the normal distribution of a specified variable. It is used to determine the probability of a random variable falling within a specified range of values. This function is commonly used in finance and scientific research.


    The NORM.S.DIST function returns the standard normal cumulative distribution function. It calculates the probability that a random variable with a standard normal distribution is less than or equal to x. This function is commonly used in statistical analysis and hypothesis testing.


    The STDEV.P function is a statistical function that calculates the standard deviation of a population based on a sample of numerical data. It is commonly used to measure the amount of variation or dispersion in a dataset. The formula assumes that the input values represent the entire population, rather than a sample. If the input values represent a sample, you should use the STDEV.S function instead.


    The AVERAGE function calculates the average (arithmetic mean) of the values passed to it. It is commonly used to find the average of a range of cells containing numerical data.

Learn More

You can learn more about the NORM.INV Google Sheets function on Google Support.