The Excel GAUSS function returns the probability that a standard normal value falls between 0 and z — that is, NORM.S.DIST(z,TRUE) minus 0.5. It gives the area under the bell curve from the mean out to z standard deviations.
Syntax
| Argument | Description | |
|---|---|---|
z | Required | The number of standard deviations from the mean. Any real number; negative z mirrors the result (GAUSS is an odd function). |
How to use it
GAUSS is a convenience for a calculation analysts do constantly: the area under the standard normal curve from the centre (0) out to z. It is simply NORM.S.DIST(z, TRUE) − 0.5:
Because the normal curve is symmetric, GAUSS(0) is 0 and the function is odd: GAUSS(−z) = −GAUSS(z). To turn the result into a two-tailed probability (the area within ±z), double it: the famous “68–95–99.7” rule comes straight out of 2×GAUSS(1), 2×GAUSS(2), and 2×GAUSS(3).
Tip: 2*GAUSS(1) ≈ 0.6827, 2*GAUSS(2) ≈ 0.9545, and 2*GAUSS(3) ≈ 0.9973 — the proportion of data within one, two, and three standard deviations of the mean.
Try it: interactive demo
Pick a GAUSS example to see the formula and its result.
Practice workbook
Frequently asked questions
What exactly does GAUSS return?
NORM.S.DIST(z,TRUE) − 0.5.How is GAUSS related to NORM.S.DIST?
NORM.S.DIST(z,TRUE) gives the area to the left of z (including the 0.5 below the mean). GAUSS strips off that 0.5, leaving just the slice from 0 to z.What does GAUSS return for a negative z?
GAUSS(−2) = −GAUSS(2) = −0.4772. GAUSS(0) is exactly 0.How do I get a two-tailed probability?
2*GAUSS(z) is the area within ±z. This produces the empirical rule values 0.6827, 0.9545, and 0.9973 for z = 1, 2, and 3.Master functions like this in one day
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