The Excel NORM.INV function returns the inverse of the normal cumulative distribution — given a probability, a mean, and a standard deviation, it returns the value x at which that cumulative probability occurs.
Syntax
| Argument | Description | |
|---|---|---|
probability | Required | A probability corresponding to the normal distribution, between 0 and 1 (exclusive). |
mean | Required | The arithmetic mean of the distribution. |
standard_dev | Required | The standard deviation of the distribution. Must be greater than 0. |
How to use it
NORM.INV is the reverse of NORM.DIST: feed it a cumulative probability and it returns the value x below which that proportion of the distribution lies.
It's the natural tool for percentiles, control limits, and confidence bounds: “what value marks the 95th percentile of this normal distribution?” The probability must be strictly between 0 and 1, and the standard deviation must be positive.
Round-trip check: NORM.INV undoes NORM.DIST. Since NORM.DIST(42,40,1.5,TRUE) is ~0.9088, NORM.INV(0.9088,40,1.5) returns ~42. For the standard normal (mean 0, sd 1) use NORM.S.INV.
Try it: interactive demo
Pick a NORM.INV example to see the formula and its result.
Practice workbook
Frequently asked questions
What does NORM.INV actually return?
x for which the normal cumulative probability equals the probability you supply. Given probability 0.95 it returns the 95th-percentile value of that distribution.How is NORM.INV related to NORM.DIST?
NORM.DIST turns a value into a cumulative probability; NORM.INV turns a cumulative probability back into a value. Round-tripping returns the original number.Why do I get a #NUM! error from NORM.INV?
#NUM!.How do I get the 95th percentile of a normal distribution?
=NORM.INV(0.95, mean, standard_dev). For a standard normal (mean 0, sd 1) the shortcut is =NORM.S.INV(0.95), which is about 1.645.Master functions like this in one day
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