NORM.S.INV Function

Excel Functions › Statistical

Excel 2010+ Statistical

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.


Quick answer:
=NORM.S.INV(0.8413) z-score for an 84.13% cumulative ~1

Syntax

=NORM.S.INV(probability)
ArgumentDescription
probabilityRequiredA 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).

=NORM.S.INV(0.8413) // ~1 (z for 84.13% to the left)
=NORM.S.INV(0.975) // ~1.96 (two-tailed 95%)

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.

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Live demo

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Result:

Practice workbook

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Frequently asked questions

What does NORM.S.INV return?
The z-score for which the standard normal cumulative probability equals the value you supply. For 0.975 it returns about 1.96 — the familiar critical value for a two-tailed 95% interval.
How is NORM.S.INV related to NORM.S.DIST?
They are inverses. 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?
For a two-tailed 95% interval use =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?
The probability argument must be strictly between 0 and 1. Supplying exactly 0 or 1, a negative number, or a value above 1 produces #NUM!.

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