Cotangent Calculator

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.