Cotangent Calculator
Get the cotangent instantly.
Result
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.
Worked example
Find cot 22°. First, tan 22° ≈ 0.404026. Then the reciprocal is 1 ÷ 0.404026 ≈ 2.475087, which is what the tool prints: 2.475087. Practical reading: for a ramp rising at 22°, every 1 m of height needs about 2.475 m of horizontal run, so a 3 m rise needs 3 × 2.475087 ≈ 7.43 m of run.
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.
About this calculator
The cotangent of an angle θ is defined as cot(θ) = cos(θ)/sin(θ) = 1/tan(θ) — the ratio of the adjacent side to the opposite side in a right triangle. Unlike tangent, which shoots to infinity as an angle approaches 90°, cotangent instead approaches zero there, and it becomes undefined at 0° and 180°, where sine is zero. This inverse behavior makes cotangent the more natural choice whenever a problem is framed around "how much horizontal run per unit of vertical rise," rather than the reverse.
Carpenters and roofers use cotangent-based relationships when converting between roof pitch (rise over run) and its angle, surveyors use it to compute horizontal distances from a measured angle of elevation, and it appears in electrical engineering when converting between reactance and resistance in AC circuit phase calculations. It is also one of the building blocks of the identity 1 + cot²(θ) = csc²(θ), used to simplify trigonometric expressions in calculus.
This calculator takes an angle in degrees and returns its cotangent value directly.
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