The Excel NORM.S.INV function returns the inverse of the standard normal cumulative distribution — given a probability, it returns the z-score below which that proportion of the curve lies.
Syntax
| Argument | Description | |
|---|---|---|
probability | Required | A probability corresponding to the standard normal distribution, between 0 and 1 (exclusive). |
How to use it
NORM.S.INV is the reverse of NORM.S.DIST: hand it a cumulative probability and it returns the z-score at that point on the standard normal curve (mean 0, standard deviation 1).
This is the function behind critical z-values for confidence intervals and hypothesis tests: NORM.S.INV(0.975) ≈ 1.96 and NORM.S.INV(0.95) ≈ 1.645. The probability must be strictly between 0 and 1.
Round-trip check: NORM.S.INV undoes NORM.S.DIST. Since NORM.S.DIST(1,TRUE) is ~0.8413, NORM.S.INV(0.8413) returns ~1. For a non-standard mean/sd use NORM.INV.
Try it: interactive demo
Pick a NORM.S.INV example to see the formula and its result.
Practice workbook
Frequently asked questions
What does NORM.S.INV return?
How is NORM.S.INV related to NORM.S.DIST?
NORM.S.DIST turns a z-score into a cumulative probability; NORM.S.INV turns that probability back into the z-score.What z-score corresponds to a 95% confidence interval?
=NORM.S.INV(0.975) ≈ 1.96. For a one-tailed 95% bound use =NORM.S.INV(0.95) ≈ 1.645.Why does NORM.S.INV give a #NUM! error?
#NUM!.Master functions like this in one day
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