COT in Excel: Calculate Cotangent with Radians and Zero Checks

• 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 COT reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=COT(number)

The required argument is an angle in radians. Its absolute value must be less than 2^27, or 134217728. Microsoft documents #NUM! outside that restriction and #VALUE! for a nonnumeric argument.

Convert degree inputs with *PI()/180 or RADIANS. A number format containing a degree symbol does not change the stored number’s unit. Cotangent is a ratio, mathematically COS(angle)/SIN(angle) wherever defined.

Enter degree values 30, 45, 60, 120, −45 in A2:A6. In B2 enter =COT(A2*PI()/180) and fill down. Expected values are approximately 1.732050808, 1, 0.577350269, −0.577350269, −1.

The sign change reflects the circular position. Values greater than one are valid; cotangent is not bounded like sine and cosine. Keep degrees clearly labeled beside the converted formula.

For a right-triangle model with vertical rise 12 and angle 35 degrees measured from horizontal:

=12*COT(35*PI()/180)

Expected horizontal run: approximately 17.137776081. Cotangent is adjacent/opposite, so multiplying the rise by cotangent recovers the run. Using the hypotenuse as the 12 would describe a different model.

The reciprocal check is =17.137776080905375*TAN(35*PI()/180), approximately 12. In an actual sheet, reference the unrounded calculated run instead of retyping a displayed approximation.

At 60 degrees, these formulas are expected to agree at approximately 0.577350269:

=COT(60*PI()/180)
=1/TAN(60*PI()/180)
=COS(60*PI()/180)/SIN(60*PI()/180)

The TAN, COS and SIN relationships are mathematical identities on their permitted inputs. They do not guarantee identical native rounding or error behavior at every singular or extreme value.

At an angle of 90 degrees, cotangent is mathematically zero while tangent is undefined. A reciprocal-of-tangent rewrite therefore introduces an intermediate that is mathematically problematic even though cotangent itself has a zero there.

=ACOT(COT(225*PI()/180))*180/PI() is expected to return approximately 45 degrees, not 225. ACOT selects its principal branch; a cotangent ratio cannot recover the original turn or periodic phase.

Retain the source angle when full-circle identity matters. Do not infer equivalence of two directions solely from equal cotangents.

Mathematically COT is undefined at integer multiples of pi. Only the literal-zero error is explicitly pinned above; using PI() to construct another multiple can leave a finite representation error and a very large output. That does not make the exact mathematical singularity well defined.

Use valid nearby controls, explicit units and a justified application tolerance. The argument limit is documented support behavior, not evidence of uniformly high accuracy right up to the boundary.

• Microsoft COT 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.