# Cotangent Calculator

URL: https://speedycalculator.com/calculators/math/cot/
Last updated: 2026-10-30

> The cotangent calculator finds cot α for any angle in degrees, radians or multiples of π, with the exact value for multiples of 15° and the five other trigonometric functions of the same angle.

## Inputs

- Angle unit
- Angle α

## Results

- cot(α)
- sin(α)
- cos(α)
- tan(α)
- csc(α)
- sec(α)

## Formula

```
cot α = 1 / tan α = cos α / sin α = adjacent / opposite
Range: all real numbers · Domain: α ≠ k·180° · Period: π (180°)
```

## Explanation

The cotangent is the reciprocal of the tangent: adjacent over opposite. It equals tan(90° − α) and appears in surveying, in the identity 1 + cot²α = csc²α and in complex analysis.

### How to use the Cotangent Calculator

- **Angle unit**
- **Angle α**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Enter the angle and pick its unit. The angle is converted to radians and cot is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.

## Worked example

Inputs — Angle unit: Degrees (°); Angle α: 30.

Results — **cot(α) = 1.732050808**; sin(α) = 1/2 ≈ 0.5; cos(α) = √3/2 ≈ 0.8660254038; tan(α) = √3/3 ≈ 0.5773502692; csc(α) = 2; sec(α) = 1.154700538.

## Key terms

- **Cotangent**: cot α = 1 / tan α = cos α / sin α = adjacent / opposite.
- **Exact value**: A value written with integers and square roots instead of decimals.

## FAQ

**What is cot 45°?**
1.

**When is cotangent undefined?**
When sin α = 0: at 0°, 180°, 360°…

**What is cot 90°?**
0, because cos 90° = 0.

**Is cot the same as arctan?**
No – cot is 1/tan; arctan is the inverse of tan.


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)
- [Wolfram MathWorld – Cotangent](https://mathworld.wolfram.com/Cotangent.html)