The Excel PHI function returns the value of the standard normal probability density function (the bell curve's height) at a given z-value.
Syntax
| Argument | Description | |
|---|---|---|
x | Required | The z-value (number of standard deviations from the mean) at which to evaluate the standard normal density. |
How to use it
PHI gives the height of the standard normal curve at a point x — not a probability, but the density. It evaluates φ(x) = e-x²/2 / √(2π).
The density is highest at the mean (x=0) and is symmetric, so PHI(-1) equals PHI(1). PHI is identical to NORM.DIST(x,0,1,FALSE) — the standard normal density without the cumulative flag.
Density, not probability. PHI returns the curve's height, which can exceed common intuition about “probabilities” only in that it is never itself a probability. For the area under the curve (an actual probability) use NORM.S.DIST or GAUSS.
Try it: interactive demo
Pick a PHI example to see the formula and its result.
Practice workbook
Frequently asked questions
What does PHI actually return?
x — the value e-x²/2/√(2π). It is a density, not a probability.Is PHI the same as NORM.DIST?
NORM.DIST(x,0,1,FALSE) — the standard normal density. For a general mean and standard deviation, or for cumulative probabilities, use NORM.DIST directly.What is the maximum value PHI can return?
x=0, where PHI(0) ≈ 0.3989 (which is 1/√(2π)). The density falls off symmetrically on both sides.How is PHI related to GAUSS?
GAUSS gives the area between the mean and x (a probability). Both were added in Excel 2013 to round out the standard normal toolkit.Master functions like this in one day
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