NORM.INV Function

Excel Functions › Statistical

Excel 2010+ Statistical

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.


Quick answer:
=NORM.INV(0.9088,40,1.5) value at the 90.88th percentile ~42

Syntax

=NORM.INV(probability, mean, standard_dev)
ArgumentDescription
probabilityRequiredA probability corresponding to the normal distribution, between 0 and 1 (exclusive).
meanRequiredThe arithmetic mean of the distribution.
standard_devRequiredThe 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.

=NORM.INV(0.9088,40,1.5) // ~42 (the 90.88th percentile)
=NORM.INV(0.5,40,1.5) // median = the mean = 40

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.

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Frequently asked questions

What does NORM.INV actually return?
The value 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?
They are inverses. 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?
The probability must be strictly between 0 and 1, and the standard deviation must be greater than 0. A probability of exactly 0 or 1, or a non-positive standard deviation, triggers #NUM!.
How do I get the 95th percentile of a normal distribution?
Use =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.

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Related functions: NORM.DIST · NORM.S.INV · NORM.S.DIST · STANDARDIZE · PERCENTILE.INC · MEDIAN