ACOT Function (Gnumeric)

Gnumeric’s ACOT returns an inverse-cotangent angle in radians. For a positive ratio, =DEGREES(ACOT(1)) has the expected result 45 degrees. There is an important cross-software difference for negative ratios: the Gnumeric 1.12.62 implementation gives ACOT(-1) = -PI()/4, so the corresponding expected degree result is -45, not Excel’s 135.

This branch was checked in Gnumeric’s tagged numerical source. The values here were independently calculated from that implementation’s mathematical rule; they were not observed in a running Gnumeric application.

=ACOT(x)

x is the one required cotangent ratio, supplied as a real number or numeric cell reference. There is no optional mode argument. The Gnumeric manual documents the one-argument function, but its short synopsis does not state the principal-angle interval. The tagged implementation supplies the missing detail for finite inputs:

• For a nonzero x, it computes ATAN(1/x).
• For x=0, it returns PI()/2.

Positive finite ratios therefore produce acute positive angles. Negative finite ratios produce negative angles between -90 and 0 degrees. Zero is a special case with a 90-degree result. This convention has a jump at zero when approached from the negative side; it is not the continuous 0-to-180-degree convention used by Excel.

The examples use English function names and decimal points. ACOT itself has one argument; the multi-argument IF example later uses commas and may need the separators accepted by your installed locale. The source check is pinned to Gnumeric 1.12.62, not a claim about the first version that introduced ACOT.

Enter the ratios below in A2:A6. Enter =DEGREES(ACOT(A2)) in B2 and fill down. Format B to display several decimals rather than expecting exact visual equality at every last digit.

For x=2, the independent check is ATAN(0.5), approximately 0.463647609 radians. For x=-2, ATAN(-0.5) gives the negative angle. The negative rows are essential compatibility tests, not merely extra examples of the positive case.

Suppose a right triangle has horizontal run 4 metres and vertical rise 2 metres. Put run in A10 and rise in B10. The cotangent ratio is run/rise, so enter:

=DEGREES(ACOT(A10/B10))

Expected result: 26.565051177 degrees. The positive-input check =DEGREES(ATAN(B10/A10)) gives the same mathematical angle. The metres cancel in the ratio; the returned degree value describes the angle rather than a length.

Check nonzero rise before dividing. The illustrative guard =IF(B10=0,"Check rise",DEGREES(ACOT(A10/B10))) covers that one numeric condition, not all invalid inputs. If both measurements are zero, there is no defined right-triangle angle. These are teaching calculations, not a validation of a real surveying or structural design procedure.

Microsoft’s ACOT reference specifies a principal angle from 0 to pi radians. To normalize Gnumeric’s signed negative results into that convention for finite numeric input in A2, use:

=DEGREES(IF(A2<0,ACOT(A2)+PI(),ACOT(A2)))

With A2=-1, the expected normalized result is 135 degrees: -45 + 180. With A2=-2, it is approximately 153.434948823 degrees. Positive inputs and zero retain their ACOT results. This is an explicit mathematical conversion, not a claim that the two applications use identical ACOT implementations.

The correction must follow the input sign; blindly adding 180 degrees to every result would break positive cases. Document the angle convention alongside the formula so a later editor does not remove the adjustment as “unnecessary.”

For a nonzero ratio such as 2, =COT(ACOT(2)) is mathematically close to 2. This checks the inverse relationship, but it cannot by itself distinguish different principal branches: cotangent repeats every pi radians. Both -45 and 135 degrees have cotangent -1.

When a full two-coordinate direction matters, use a deliberately specified ATAN2 workflow instead of hoping that one ratio preserves a quadrant. Gnumeric documents ATAN2(x,y) with the x-coordinate first. Do not paste a programming-language atan2(y,x) call without translating its argument order. A zero-length vector is not a direction.

Radians mistaken for degrees: a result near 0.785398 for a ratio of 1 is a radian value. Wrap ACOT in DEGREES for the 45-degree result.

Negative angles differ from Excel: this can be a branch convention, not a calculation defect. Use the signed Gnumeric result or explicitly normalize it, according to the problem you intend to solve.

Inputs near zero or very large magnitudes: expect sensitivity near the branch jump and finite-precision effects at extreme magnitudes. Only ordinary finite real inputs are used in the checked examples. Text, booleans, missing values, infinity and exact native error formatting were not tested here.

A round-trip looks correct but the direction is wrong: an inverse identity does not establish the desired principal interval. Check signed examples and the application’s documented convention separately.

COT, ATAN, ATAN2, RADIANS, DEGREES, PI.

The official Gnumeric reference establishes the function’s purpose and argument structure. The arguments and worked examples were editorially reviewed and the stated expected results were independently calculated. The tagged Gnumeric 1.12.62 numerical implementation was additionally checked for ACOT’s signed branch and zero-input special case.

Review date: 2026-10-12. No native application run: the worked outputs are documentation-based or independently calculated expectations, not measurements from installed Gnumeric. Ordinary numeric cases and the stated text-construction examples are checked; blank/text coercion, machine extremes and workbook round trips are not certified. The formula editor in your installed version is the authority for localized separators.

Example-check record · Editorial standards.