Cosine calculator
Enter an angle and get its cosine straight away. For special angles, such as 30°, 45° and 60°, you also see the exact value, for example cos(60°) = 1/2.
In degrees or radians (choose above). pi/3 works too.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
What is the cosine?
In a right-angled triangle, the cosine of an angle is the adjacent side divided by the hypotenuse. On the unit circle it is the x-coordinate of the point at that angle, which is why the cosine is always between −1 and 1.
Degrees or radians?
A full turn is 360° or 2π radians, so 60° = π/3 rad. Enter the angle in degrees or radians (choose above). Expressions such as pi/3 or 2pi/5 work too. The result is the same either way; only the unit of the angle differs.
Useful values
cos(0°) = 1, cos(60°) = 1/2, cos(90°) = 0 and cos(180°) = −1. To find the angle that belongs to a cosine, use the arccos calculator. For sine, cosine and tangent together, use the trigonometry calculator.
Exact values to remember
| Angle | cos | Decimal |
|---|---|---|
| 0° | 1 | 1 |
| 30° | √3/2 | 0.8660 |
| 45° | √2/2 | 0.7071 |
| 60° | 1/2 | 0.5 |
| 90° | 0 | 0 |
| 180° | −1 | −1 |
A practical example
A ladder of 4 m leans against a wall at an angle of 70° with the ground. It reaches 4 × cos(70°) ≈ 1.37 m from the wall along the floor. In a right-angled triangle the cosine gives the adjacent side as a fraction of the hypotenuse, so you multiply by the hypotenuse to find the adjacent side.
The cosine rule
In any triangle, c² = a² + b² − 2ab · cos(C). That makes the cosine the tool for triangles that are not right-angled. To go from a cosine back to the angle, use the arccos calculator; for a right-angled triangle with two known sides, the right triangle calculator is quicker.
Frequently asked questions
What is cos 0 and cos 90?
cos(0°) = 1 and cos(90°) = 0. The cosine starts at 1, falls to 0 at 90°, reaches −1 at 180°, returns to 0 at 270° and is back at 1 at 360°.
Why does my calculator give a different answer?
Almost always because it is in the wrong mode. cos(60) is 0.5 in degree mode, but about −0.952 in radian mode. Choose the unit above the field here, and the result follows.
What is the cosine of a negative angle?
The same as the cosine of the positive angle: cos(−x) = cos(x). Cosine is an even function, so cos(−60°) is 1/2 as well.
When is the cosine negative?
For angles between 90° and 270°, where the point on the unit circle is left of the vertical axis. cos(120°) = −1/2.