ID EN
#Statistical

PHI

Excel Functions

Get value of the density function for standard normal distribution

Syntax

EXCEL
=PHI(x)

Arguments

Parameter Description
x The value (z-score) for which you want the density of the standard normal distribution.

Return Value

The value of the standard normal density function at the given point

Details

The PHI function calculates the value of the probability density function for a standard normal distribution at a given point. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The PHI function is often used in statistical analysis, data science, and financial modeling to understand how likely a value is within a standard normal distribution. For example, the following formula returns the value of the standard normal density function at 1: The PHI function takes a single argument, x, and returns the value of the standard normal density function at that point: The PHI function can be used to calculate PDF values for normal distributions with different means and standard deviations. For example, suppose you have a list of values from a

Examples

Example 1

For example, the following formula returns the value of the standard normal density function at 1:

EXCEL
=PHI(1) // returns 0.241970725
Example #1 - Basic usage

The PHI function takes a single argument, x, and returns the value of the standard normal density function at that point:

EXCEL
=PHI(-2) // returns 0.053990967
=PHI(-1) // returns 0.241970725
=PHI(0)  // returns 0.398942280
=PHI(1)  // returns 0.241970725
=PHI(2)  // returns 0.053990967
Example #2 - Using z-scores

The PHI function can be used to calculate PDF values for normal distributions with different means and standard deviations. For example, suppose you h

EXCEL
=PHI(STANDARDIZE(93,83,5)) // returns 0.0539909665
Example #2 - Using z-scores

The z-score of a value, which measures how many standard deviations a value is from the mean, can be calculated using the STANDARDIZE function:

EXCEL
=STANDARDIZE(93,83,5) // returns 2
Example #2 - Using z-scores

or manually like this:

EXCEL
z = (value - mean) / stdev
Example #3 - Error handling

The PHI function returns the #VALUE! error if x is not numeric.

EXCEL
=PHI("apple") // returns #VALUE!

See Also

NORM.S.DIST NORM.DIST NORM.INV STANDARDIZE