Cotangent Calculator

How it is calculated

The angle is entered in degrees. The tool converts it to radians, finds the tangent and returns its reciprocal: cot θ = 1 ÷ tan θ (the same as cos θ ÷ sin θ). The answer is a unitless ratio, adjacent side over opposite side, shown to 6 decimal places. Negative angles and angles above 360° are fine, because cotangent repeats every 180°: cot(θ + 180°) = cot θ. Where the tangent is practically zero, which means at 0°, 180°, 360° and every multiple of 180°, the cotangent is undefined and the tool returns nothing. At 90° and 270° the tangent is huge, so the cotangent prints as 0.000000. An empty box also gives no result.

Common mistakes

• Entering radians. The box expects degrees, so 0.3840 for 22° is read as 0.384 degrees and gives a cotangent near 149.
• Trying 0° or 180° and treating the empty result as a fault. The cotangent is undefined there, so no number exists.
• Mixing up cotangent with arctangent. cot θ is 1 ÷ tan θ, a ratio, whereas tan⁻¹ gives an angle back; they are different functions.
• Dividing run by rise the wrong way round. Cotangent is adjacent ÷ opposite, so a shallow angle gives a large value (cot 5° ≈ 11.43) and a steep angle a small one.
• Assuming it falls to −∞ or +∞ at 90°. There the cotangent is simply 0; it is the tangent that blows up.