Cotangent Calculator (cot)

The cotangent is calculated as the ratio of the adjacent side to the opposite side in a right triangle: cot(α) = adjacent / opposite. Equivalently, cot(x) = cos(x) / sin(x), or cot(x) = 1 / tan(x). Enter your angle in degrees or radians above and the calculator computes it for you.

Cotangent is the reciprocal of tangent, not the inverse. cot(x) = 1 / tan(x). The inverse of tangent is arctan (also written tan⁻¹), which returns an angle when given a ratio. Cotangent returns a ratio when given an angle.

You can use either degrees or radians with the cotangent function — both are valid. Degrees are more common in everyday geometry, while radians are standard in higher mathematics and physics. This calculator supports both; simply select your preferred unit.

Yes, for common angles you can use known values. For example, cot(45°) = 1, cot(30°) = √3 ≈ 1.732, and cot(60°) = 1/√3 ≈ 0.577. For other angles, use the formula cot(x) = cos(x) / sin(x) with known sine and cosine values.

Most standard calculators do not have a dedicated cot button. Instead, calculate tan(x) and take its reciprocal: cot(x) = 1 ÷ tan(x). Alternatively, use the formula cot(x) = cos(x) ÷ sin(x). This online calculator computes cot(x) directly from your angle.

The cotangent of 0° is undefined. At 0° (or 0 radians), sin(0) = 0, and since cot(x) = cos(x)/sin(x), dividing by zero makes the result undefined. Similarly, cot(x) is undefined at every multiple of 180° (or π radians).

Cotangent is widely used in trigonometry, physics, and engineering. Applications include calculating angles of elevation or depression, analyzing wave behavior, solving right triangle problems, and working with polar coordinates. It also appears in calculus as the derivative of cot(x) = −csc²(x).

The domain of cot(x) is all real numbers except multiples of π (i.e., x ≠ nπ for any integer n), because the function is undefined where sin(x) = 0. The range of cotangent is all real numbers (−∞, ∞), meaning cot(x) can take any value.