GAUSS Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this is a verified release, not a final supported version.
• Scope: Desktop Calc, English function names and semicolon-separated formulas. Locale and file-format mappings may differ.
• Checked: October 14, 2026. Eight reference formulas and the listed boundary cases were recalculated in 4.1.16 on Linux x86-64, Build 9816, using generated native ODF-formula input. Source and independent mathematics were also checked.

GAUSS returns Φ(z)−0.5, where Φ is the standard-normal cumulative distribution. It is the signed probability area from zero to z. Its value is negative when z is negative, so it is not itself a general lower-tail cumulative probability. Release implementation.

=GAUSS(Z)

Exactly one numeric standardized value is used. Z=0 gives zero. For a finite real z the exact value lies between −0.5 and 0.5. The source evaluates a dedicated normal-area approximation, and finite-precision results can round to either limiting half.

These eight formulas were recalculated in the stated 4.1.16 build using generated native ODF-formula input. Saved numeric results agree with independent high-precision calculations; values below are rounded to twelve decimal places. The comparison concerns stored values, not a claim that every display format prints the same digits.

For z=1, =GAUSS(1) gives approximately 0.341344746069, the probability area from the mean to one standard deviation above it. The lower-tail probability is =0.5+GAUSS(1), approximately 0.841344746069.

For z=−1, GAUSS returns approximately −0.341344746069; adding 0.5 gives approximately 0.158655253931. Taking an absolute value without checking the intended event would erase which side of the mean was requested.

For a standard-normal variable Z, P(a<Z≤b)=GAUSS(b)−GAUSS(a), provided a≤b. The independent interval =GAUSS(2)-GAUSS(1) is approximately 0.135905121983. The symmetric interval =2*GAUSS(1) is approximately 0.682689492137.

For a normal quantity with mean μ and positive standard deviation σ, standardize a cutoff x as (x−μ)/σ first. For example, a cutoff of 82 with mean 70 and standard deviation 8 has z=1.5; the probability below the cutoff is 0.5+GAUSS(1.5). These probability interpretations require a normal model, not merely numeric inputs.

The right tail can be written mathematically as 0.5−GAUSS(z), but subtracting nearly equal halves loses precision for extreme positive z. A saturated result is not proof that the true tail probability is exactly zero.

Negative arguments and negative results are ordinary, valid behavior. A returned 0.5 at a large positive input indicates finite precision in this calculation, not a probability of only one half below that cutoff; the lower-tail conversion still adds 0.5.

GAUSS and PHI are different functions: PHI gives a density height, whereas GAUSS gives a signed area. Do not multiply or divide by a standard deviation without first identifying which quantity the formula returns.

The following boundary formulas were recalculated in the same named method. H5 and H6 are deliberately empty cells where referenced. An error display remains an error even if the underlying ODS numeric attribute stores zero.

Tested import limitation

The separate XLSX input produced an unresolved _xlfn.GAUSS identifier and #NAME? for these cases. Those results identify an import-path failure, not the native function’s calculation. The successful results above came from generated ODF formulas followed by hard recalculation; they were not manually typed.

• NORMSDIST
• NORMDIST
• STANDARDIZE

• Function-specific release entry
• Numeric helper or argument collection

The retained input and saved ODS preserve the tested formula identities. A stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence is limited to the eight reference formulas and listed boundary cases in this exact release and method. Composite explanatory examples are independent calculations unless listed among those cases; other releases, locales and extreme-parameter accuracy were not established.