ACOT in Excel: Use the Correct Principal Arccotangent Branch

• Introduced: Microsoft marks the function as introduced in Excel 2013. Version-marker reference.
• Availability: official help 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.
• Checked: October 14, 2026; official ACOT reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=ACOT(number)

The required input is a real cotangent value. Microsoft specifies a principal output between zero and pi radians and documents #VALUE! for a nonnumeric argument. The result can be converted with 180/PI() or DEGREES.

The input itself is a ratio. Do not multiply it by PI()/180 before applying the inverse. That would change the supplied cotangent rather than convert the resulting angle.

Enter −2, −1, 0, 1, 2 in A2:A6. In B2 put =ACOT(A2) and fill down. Expected radian results are approximately 2.677945045, 2.356194490, 1.570796327, 0.785398163, 0.463647609.

For the middle controls −1, 0 and 1, the expected degree results are 135, 90 and 45. Zero is a valid cotangent input and produces a right angle; it is not a reason to divide by zero inside a substitute formula.

=ACOT(-1)*180/PI()
=ATAN(1/-1)*180/PI()

Expected results are 135 and −45 degrees. Both angles have cotangent −1, but they belong to different principal branches. ATAN of a reciprocal does not reproduce ACOT for negative inputs.

For positive input 2 the shortcut does agree, returning approximately 0.463647609 radians. Agreement in one positive test therefore does not establish equivalence over all real numbers. Include zero and a negative input when checking a replacement.

Using B2:B6 from the first table, fill =COT(B2) down in C2:C6. Expected reconstructed ratios are approximately −2, −1, 0, 1, 2. The zero can carry a tiny floating-point residual because the stored right-angle representation is approximate.

Keep B’s radian values as the inputs to COT. Feeding degree-converted display values directly into COT would mix units.

In a stated right triangle, an adjacent side of 12 and opposite side of 5 give cotangent 12/5. Use =ACOT(12/5)*180/PI(), with expected acute angle approximately 22.619864948 degrees.

That positive-length triangle selects the acute branch naturally. A signed coordinate problem needs its axis and quadrant convention stated separately; a cotangent ratio by itself has already discarded full-turn information. Use ATAN2 when both original coordinates are available and direction is the goal.

Check ratio versus angle units, the desired branch and whether a shortcut introduced an unnecessary reciprocal. The documented 0-to-pi interval identifies the branch, but this guide does not certify exact native endpoint rounding for extreme finite inputs. Preserve the source ratio and compare ordinary positive, zero and negative controls before relying on an imported formula.

• Microsoft ACOT reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.