ACOT

Quirk found

Category: Math and trigonometry · Last tested 2026-09-04

Real compatibility results for the ACOT function: executed in Excel for the web, Google Sheets and LibreOffice Calc, with desktop Excel behavior from Microsoft’s official documentation (we do not run desktop Excel — Excel for the web is a different application and is executed separately). Syntax and links to that documentation are below.

Support matrix

Engine	Documented	Live-tested	Verdict
Excel (desktop)	Yes	No — documented only	n/a
Excel for the web	—	Yes (recalc, 2026-09-01)	Supported, behaves as documented
Google Sheets	Yes	Yes (Drive import, 2026-08-31)	Quirk found
LibreOffice Calc	Yes	Yes (25.8.7.3, 2026-09-04)	Supported, behaves as documented

LibreOffice version history

We executed the same test cases under each LibreOffice release to show exactly when ACOT’s support changed — not documentation claims, real results.

LibreOffice version	Verdict	Tested
24.2.0.3	Supported, behaves as documented	2026-09-04
24.8.7.2	Supported, behaves as documented	2026-09-04
25.2.0.3	Supported, behaves as documented	2026-09-04
25.8.7.3	Supported, behaves as documented	2026-09-04

Why isn’t ACOT working in Google Sheets?

ACOT runs in Google Sheets, but our executed cases show it does not match Excel’s documented behavior on every input (the failing cases are listed on this page). If a formula that behaves one way in Excel gives you a different answer in Sheets, compare your usage against those cases before assuming your data is wrong.

Discovered quirks

=ROUND(ACOT(-2),9) on Google Sheets returned -0.463647609, but the documented/expected result is 2.677945045.
Provenance
Excel documents the result is in the range 0 to pi, so for a negative argument ACOT(-2) = pi + atan(1/-2) = pi - 0.4636476090008061 = 2.677945044588987 -> 2.677945045 at 9 dp, NOT the negative -0.4636 that atan(1/x) alone would give; MISMATCH vs expected: expected 2.677945045, got -0.463647609

Executed test cases

Excel for the web (executed 2026-09-01 via OneDrive recalculation)

These values come from Excel for the web, not from desktop Excel. They are two different implementations of the calculation engine, and this run measured only the web one: the corpus was uploaded to OneDrive as .xlsx, recalculated by Excel for the web on open, and downloaded again for readback. Excel for the web is a rolling service with no pinnable version, so the run is identified by its date. Where a value here disagrees with the Expected column — which is Microsoft’s documentation of the desktop product — we cannot tell you whether the web engine diverges from the desktop one or the documentation is wrong about both, because we do not run desktop Excel.

Formula	Description	Result	Expected	Verdict
=ROUND(ACOT(2),4)	Microsoft's documented worked example: arccotangent of 2 in radians	0.4636	0.4636 Provenance Microsoft's page publishes this example's result as 0.4636. Independently verified: acot(2) = atan(1/2) = 0.4636476090008061 -> 0.4636 at 4 dp. (Excel's ACOT returns the principal value in 0..pi, which for a positive argument agrees with atan(1/x))	Matched
=ROUND(ACOT(0),9)	The arccotangent of zero, the midpoint of the documented 0..pi output range	1.570796327	1.570796327 Provenance Excel documents "The returned angle is given in radians in the range 0 (zero) to pi", and cot(pi/2) = 0, so ACOT(0) = pi/2. Independently verified: math.pi/2 = 1.5707963267948966 -> 1.570796327 at 9 dp. This case distinguishes the documented 0..pi principal branch from the atan(1/x) shortcut, which is undefined at 0	Matched
=ROUND(ACOT(-2),9)	A negative argument, where the documented 0..pi range differs from atan(1/x)	2.677945045	2.677945045 Provenance Excel documents the result is in the range 0 to pi, so for a negative argument ACOT(-2) = pi + atan(1/-2) = pi - 0.4636476090008061 = 2.677945044588987 -> 2.677945045 at 9 dp, NOT the negative -0.4636 that atan(1/x) alone would give	Matched
=ACOT("abc")	A non-numeric text argument	#VALUE!	#VALUE! Provenance Excel documents: "If Number is a non-numeric value, ACOT returns the #VALUE! error value."	Matched

Google Sheets (executed 2026-08-31 via Drive import)

Google Sheets is a rolling service with no pinnable version, so this run is identified by its date. The corpus was imported to Drive as .xlsx, recalculated by Sheets, and exported back for readback.

Formula	Description	Result	Expected	Verdict
=ROUND(ACOT(2),4)	Microsoft's documented worked example: arccotangent of 2 in radians	0.4636	0.4636 Provenance Microsoft's page publishes this example's result as 0.4636. Independently verified: acot(2) = atan(1/2) = 0.4636476090008061 -> 0.4636 at 4 dp. (Excel's ACOT returns the principal value in 0..pi, which for a positive argument agrees with atan(1/x))	Matched
=ROUND(ACOT(0),9)	The arccotangent of zero, the midpoint of the documented 0..pi output range	1.570796327	1.570796327 Provenance Excel documents "The returned angle is given in radians in the range 0 (zero) to pi", and cot(pi/2) = 0, so ACOT(0) = pi/2. Independently verified: math.pi/2 = 1.5707963267948966 -> 1.570796327 at 9 dp. This case distinguishes the documented 0..pi principal branch from the atan(1/x) shortcut, which is undefined at 0	Matched
=ROUND(ACOT(-2),9)	A negative argument, where the documented 0..pi range differs from atan(1/x)	-0.463647609	2.677945045 Provenance Excel documents the result is in the range 0 to pi, so for a negative argument ACOT(-2) = pi + atan(1/-2) = pi - 0.4636476090008061 = 2.677945044588987 -> 2.677945045 at 9 dp, NOT the negative -0.4636 that atan(1/x) alone would give	Mismatch
=ACOT("abc")	A non-numeric text argument	#VALUE!	#VALUE! Provenance Excel documents: "If Number is a non-numeric value, ACOT returns the #VALUE! error value."	Matched

LibreOffice Calc 25.8.7.3 (tested 2026-09-04)

Formula	Description	Result	Expected	Verdict
=ROUND(ACOT(2),4)	Microsoft's documented worked example: arccotangent of 2 in radians	0.4636	0.4636 Provenance Microsoft's page publishes this example's result as 0.4636. Independently verified: acot(2) = atan(1/2) = 0.4636476090008061 -> 0.4636 at 4 dp. (Excel's ACOT returns the principal value in 0..pi, which for a positive argument agrees with atan(1/x))	Matched
=ROUND(ACOT(0),9)	The arccotangent of zero, the midpoint of the documented 0..pi output range	1.570796327	1.570796327 Provenance Excel documents "The returned angle is given in radians in the range 0 (zero) to pi", and cot(pi/2) = 0, so ACOT(0) = pi/2. Independently verified: math.pi/2 = 1.5707963267948966 -> 1.570796327 at 9 dp. This case distinguishes the documented 0..pi principal branch from the atan(1/x) shortcut, which is undefined at 0	Matched
=ROUND(ACOT(-2),9)	A negative argument, where the documented 0..pi range differs from atan(1/x)	2.677945045	2.677945045 Provenance Excel documents the result is in the range 0 to pi, so for a negative argument ACOT(-2) = pi + atan(1/-2) = pi - 0.4636476090008061 = 2.677945044588987 -> 2.677945045 at 9 dp, NOT the negative -0.4636 that atan(1/x) alone would give	Matched
=ROUND(ACOT(-0.5),9)	Arccotangent of -0.5, a negative argument between -1 and 0	2.034443936	2.034443936 Provenance Microsoft documents "The returned angle is given in radians in the range 0 (zero) to pi", so for a negative argument the result is pi + atan(1/x), not atan(1/x) alone: ACOT(-0.5) = pi + atan(1/-0.5) = pi + atan(-2) = 3.141592653589793 - 1.1071487177940904 = 2.0344439357957027 -> 2.034443936 at 9 dp. The bare atan(1/x) shortcut would give -1.107148718, which is pi lower and outside the documented 0..pi range	Matched
=ROUND(ACOT(-1),9)	Arccotangent of -1, the mirror of the documented ACOT(1) = pi/4 example	2.35619449	2.35619449 Provenance Microsoft documents "The returned angle is given in radians in the range 0 (zero) to pi", so ACOT(-1) = pi + atan(1/-1) = pi - pi/4 = 3pi/4 = 2.356194490192345 -> 2.35619449 at 9 dp. cot(3pi/4) = -1, confirming the value is a genuine arccotangent and not merely a sign flip of ACOT(1); the bare atan(1/x) shortcut would give -0.785398163, exactly pi lower	Matched
=ROUND(ACOT(-10),9)	Arccotangent of -10, a large negative argument approaching the top of the documented range	3.041924001	3.041924001 Provenance Microsoft documents "The returned angle is given in radians in the range 0 (zero) to pi", so ACOT(-10) = pi + atan(1/-10) = 3.141592653589793 - 0.09966865249116204 = 3.0419240010986313 -> 3.041924001 at 9 dp. As x -> -infinity the documented branch approaches pi from below; the bare atan(1/x) shortcut would give -0.099668652, approaching 0 from below instead	Matched
=ROUND(DEGREES(ACOT(-1)),6)	The same negative-argument arccotangent converted to degrees, where the branch choice is a 180 degree difference	135	135 Provenance Microsoft documents "The returned angle is given in radians in the range 0 (zero) to pi" and points to DEGREES for the conversion, so DEGREES(ACOT(-1)) = DEGREES(pi + atan(1/-1)) = DEGREES(3*pi/4) = 135 exactly. An engine that returns the bare atan(1/x) instead reports -45 degrees for the same cell, i.e. the same direction rotated by 180 degrees	Matched
=ROUND(ACOT(1),9)	Arccotangent of 1, the positive control where every convention agrees	0.785398163	0.785398163 Provenance Microsoft documents "The returned angle is given in radians in the range 0 (zero) to pi". For a positive argument pi + atan(1/x) would fall outside 0..pi, so the documented branch is plain atan(1/x): ACOT(1) = atan(1) = pi/4 = 0.7853981633974483 -> 0.785398163 at 9 dp. LibreOffice documents the same value for this exact formula ("=ACOT(1) returns 0.785398163397448 (PI/4 radians)"). This is the control case: it isolates the divergence to negative arguments	Matched
=ACOT("abc")	A non-numeric text argument	#VALUE!	#VALUE! Provenance Excel documents: "If Number is a non-numeric value, ACOT returns the #VALUE! error value."	Matched

Docs & syntax

Excel (desktop): official documentation
Google Sheets: official documentation
LibreOffice Calc: official documentation

Where ACOT behaves differently

ACOT of a negative number is off by pi in Google Sheets versus Excel and LibreOffice
Executed evidence: =ROUND(ACOT(-2),9) is -0.463647609 in Google Sheets but 2.677945045 in Excel for the web and in all four LibreOffice builds. The two branches differ by exactly pi, 180 degrees, with no error anywhere. Dates, per-engine provenance and the portable fix.