Cosine Calculator
Calculate the cosine of any angle in degrees or radians, with the radian conversion and the matching sine and tangent alongside.
How to use it
- Enter the angle and choose degrees or radians.
- Cosine always returns a value between −1 and 1.
- cos(0°) is 1 and cos(90°) is 0.
Examples
| cos(0°) | 1 |
| cos(60°) | 0.5 |
| cos(180°) | −1 |
Cosine is the ratio of the side adjacent to an angle to the hypotenuse: cos θ = adjacent ÷ hypotenuse. It starts at 1 when the angle is 0° and falls to 0 at 90°, the mirror image of sine's rise — which is exactly why the two are 90° out of phase.
Worked example — horizontal reach
A crane arm 12 m long is raised to 50° above horizontal. Its horizontal reach from the base is 12 × cos(50°) ≈ 7.71 m. Cosine gives the horizontal component of a length-and-angle pair, the counterpart to sine's vertical component.
Key values worth memorising
| Angle | cos θ |
|---|---|
| 0° | 1 |
| 30° | 0.8660 |
| 45° | 0.7071 |
| 60° | 0.5 |
| 90° | 0 |
Questions people ask
How is cosine related to sine?
They are the same wave shifted by 90°: cos θ = sin(θ + 90°). On the unit circle cosine is the horizontal coordinate and sine the vertical one.
Is anything sent to a server?
No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.
Last updated 17 August 2026