GAUSS in Excel: Signed Areas Around the Normal Mean

=GAUSS(z)

The required z argument is measured in standard deviations from a mean of zero. This function does not accept an arbitrary mean or standard deviation. If the original measurement has mean mu and positive scale sigma, standardize it first as (x−mu)/sigma.

Microsoft explicitly relates GAUSS(z) to NORM.S.DIST(z,TRUE)−0.5. That relation explains the sign: a negative result is a signed difference from the median, not a negative probability assigned to an event.

Enter -2, -1, 0, 1 and 2 in A2:A6. Fill down:

=GAUSS(A2)

Expected outputs are approximately -0.477249868, -0.341344746, 0, 0.341344746 and 0.477249868. Equal-magnitude scores have opposite signs.

To report the probability of falling between the mean and either endpoint without a sign, use ABS(GAUSS(A2)). For z=-1, that probability is approximately 0.341344746. Label the quantity clearly so a signed diagnostic is not confused with an ordinary event probability.

For z=1:

=0.5+GAUSS(1)
=0.5-GAUSS(1)

Expected results are 0.841344746 and 0.158655254. The first is the probability at or below 1; the second is the probability above 1 under the standard-normal model.

For a negative threshold such as -1, the same first expression gives 0.158655254. Do not replace GAUSS(-1) with its absolute value before adding 0.5; doing so would switch the percentile to the wrong side of the distribution.

The probability within z standard deviations of the mean, for nonnegative z, is:

=2*GAUSS(1)
=2*GAUSS(2)

Expected coverages are 0.682689492 and 0.954499736. If a worksheet permits a signed input but intends a symmetric distance, =2*GAUSS(ABS(A2)) makes that interpretation explicit.

The complement, =1-2*GAUSS(2), is approximately 0.045500264. It combines both tails beyond ±2. It is not the one-sided upper-tail probability.

For lower z=-0.5 and upper z=1.5:

=GAUSS(1.5)-GAUSS(-0.5)

Expected area: 0.624655260. The two added 0.5 constants cancel, so the difference of GAUSS values is the same as the difference of cumulative probabilities.

Require the upper endpoint to be at least the lower endpoint. Reversing them produces a negative oriented difference, not an ordinary interval probability. Using ABS would hide the endpoint mistake rather than clarify the intended interval.

Assume a fictional measured duration has a specified mean of 50 and standard deviation of 10. For x=65:

=GAUSS((65-50)/10)
=0.5+GAUSS((65-50)/10)

Expected values are 0.433192799 and 0.933192799. The first is the area from the mean to 65; the second is the cumulative probability up to 65 under the assumed normal model.

The normality assumption and reference parameters come from the analysis, not from GAUSS. Standardizing observed data does not by itself make the data normally distributed.

Microsoft documents #VALUE! for an invalid data type and #NUM! for an invalid numeric value. The reference does not provide a universal numeric boundary to reproduce here. Ordinary finite negative z values are valid and intentionally produce negative results.

If a result is near zero when 0.5 was expected, check whether a signed mean-to-z area was requested instead of a cumulative probability. If the result is twice the expected tail, check one-sided versus two-sided interpretation. Extreme-tail precision, text coercion, blank-cell behavior and native Excel rounding remain unverified.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical function catalog marks GAUSS as introduced in Excel 2013. The exact first build and platform-specific introduction dates are not established here.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples below were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft GAUSS reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.