Calculate cot of any angle in degrees or radians with exact common values.
Common cotangent values
| Angle | Radians | cot(θ) | Decimal |
|---|---|---|---|
| 0° | 0 | Undefined | — |
| 30° | π/6 | √3 | 1.73205081 |
| 45° | π/4 | 1 | 1.00000000 |
| 60° | π/3 | √3/3 | 0.57735027 |
| 90° | π/2 | 0 | 0.00000000 |
| 120° | 2π/3 | −√3/3 | −0.57735027 |
| 135° | 3π/4 | −1 | −1.00000000 |
| 150° | 5π/6 | −√3 | −1.73205081 |
| 180° | π | Undefined | — |
| 270° | 3π/2 | 0 | 0.00000000 |
How is cotangent computed?
The cotangent of an angle θ is the ratio of cosine to sine: cot(θ) = cos(θ) / sin(θ). Equivalently, it is the reciprocal of the tangent: cot(θ) = 1 / tan(θ). In a right triangle, cotangent equals the length of the adjacent side divided by the length of the opposite side — the inverse of tangent (opposite / adjacent).
Cotangent is undefined wherever sin(θ) = 0, which happens at θ = 0°, 180°, 360° and every integer multiple of 180° (or π in radians). At those points the ratio cos/sin divides by zero.
Frequently asked questions
What is cotangent?
Cotangent (abbreviated cot or ctg) is one of the six trigonometric functions. It is defined as cos(θ) divided by sin(θ), or equivalently 1 divided by tan(θ). In a right triangle, cot(θ) equals the length of the adjacent leg divided by the length of the opposite leg. The function is periodic with period 180° (π radians) and takes every real value between −∞ and +∞ on each period.
What is the difference between cot and tan?
Tangent and cotangent are reciprocal functions: cot(θ) = 1 / tan(θ). While tan(θ) = sin(θ)/cos(θ) (opposite over adjacent), cot(θ) = cos(θ)/sin(θ) (adjacent over opposite). Tangent is undefined where cos(θ) = 0 (at 90°, 270°, …), whereas cotangent is undefined where sin(θ) = 0 (at 0°, 180°, 360°, …). Their graphs are mirror reflections of each other with asymptotes shifted by 90°.
Why is cot(0°) and cot(180°) undefined?
At θ = 0° and θ = 180° the sine equals zero (sin 0° = 0, sin 180° = 0). Since cot(θ) = cos(θ)/sin(θ), the ratio becomes cos(θ)/0, which is division by zero and therefore undefined. The cotangent graph has vertical asymptotes at every integer multiple of 180°. Approaching those points from one side the function tends to +∞, and from the other side to −∞.
What are the values of cotangent at common angles?
The standard reference values are: cot(30°) = √3 ≈ 1.73205081, cot(45°) = 1, cot(60°) = √3/3 ≈ 0.57735027, cot(90°) = 0. For the second quadrant: cot(120°) = −√3/3, cot(135°) = −1, cot(150°) = −√3. The function is positive in the first and third quadrants, negative in the second and fourth, and repeats every 180°.
How do I convert degrees to radians before using cot?
Multiply the degree value by π/180. For example, 45° × π/180 = π/4 ≈ 0.7854 radians. Most scientific calculators and programming languages compute trigonometric functions in radians, so the conversion is needed when your input is in degrees. This tool does the conversion automatically when you choose the Degrees unit.
This tool computes the cotangent of an angle using cot(θ) = cos(θ) / sin(θ) = 1 / tan(θ). Enter the angle value, choose Degrees or Radians, and the result is shown to 8 decimal places along with the matching tangent and an exact form when the angle is a standard value. For example, cot(30°) ≈ 1.73205081 (exact √3), cot(45°) = 1, cot(60°) ≈ 0.57735027 (exact √3/3), and cot(90°) = 0. At angles where sin(θ) = 0 — that is, 0°, 180°, 360° and every multiple of 180° — the function is undefined and the tool reports “Undefined” instead of a numeric value. Preset buttons load common angles in one tap, and a copy button places the numeric result in the clipboard.