Inverse Cosine (arccos) Calculator
Calculate arccos(x) in degrees and radians, as a multiple of π, from a cosine value or from the adjacent side and hypotenuse of a right triangle.
Inverse cosine, written arccos(x) or cos⁻¹(x), answers the question "which angle has this cosine?". Enter a value between −1 and 1, or the adjacent side and hypotenuse of a right triangle, and the calculator returns the angle in degrees and radians, as an exact multiple of π when it is a standard angle, and the second angle between 0° and 360° that has the same cosine.
How to use this tool
- Choose whether you have a cosine value or two sides of a right triangle.
- Enter the value x (from −1 to 1), or the adjacent side and the hypotenuse.
- Read the angle in degrees and radians; standard angles are also shown as a multiple of π.
- Use the second angle and the general solution if you need every angle with that cosine.
Formula
θ = arccos(x), 0 ≤ θ ≤ π (0° to 180°), for −1 ≤ x ≤ 1
arccos returns the principal value: the one angle between 0° and 180° whose cosine is x. In a right triangle, x = adjacent ÷ hypotenuse. Because cos(360° − θ) = cos θ, the angle 360° − θ shares the same cosine, and every solution can be written ±θ + 360°·k. To convert, degrees = radians × 180 ÷ π.
Example
A right triangle with an adjacent side of 4 and a hypotenuse of 5 gives x = 0.8, and arccos(0.8) = 36.869898° = 0.643501 rad. The opposite side is 3 (a 3-4-5 triangle), so sin θ = 0.6 and tan θ = 0.75. With x = 0.5 the answer is exactly 60°, or π/3, and the other angle with that cosine is 300°.
Frequently asked questions
Why is arccos only defined from −1 to 1?
The cosine of any real angle lies between −1 and 1, so no real angle has a cosine of 1.2. Calculators report an error, or a complex number, for inputs outside that range.
Is cos⁻¹(x) the same as 1/cos(x)?
No. cos⁻¹ means the inverse function; 1/cos(x) is the secant, sec(x). arccos(0.5) is 60°, while 1/cos(0.5 rad) is about 1.1395.
Why does arccos only give angles from 0° to 180°?
An inverse function must return a single answer, so arccos is restricted to the range where cosine takes each value exactly once. The other angle with the same cosine, 360° − θ, is shown separately.
What are the common exact values?
arccos(1) = 0°, arccos(√3/2) = 30°, arccos(√2/2) = 45°, arccos(1/2) = 60°, arccos(0) = 90° and arccos(−1/2) = 120°. The table under the results lists them in radians too.
Last updated: 2026-10-30