Arccos Calculator
Use this calculator to find the inverse cosine (arccos, or cos-1) of a number.
What is arccos?
Arccos (written as arccos(x) or cos-1(x)) is the inverse function of cosine. It answers this question: “What angle has cosine equal to x?”
Important domain and range rules
Domain of arccos
The input must be between -1 and 1, inclusive. Any value outside that interval has no real arccos result.
- Valid: -1, -0.2, 0, 0.75, 1
- Invalid (real numbers): -1.1, 2, 5.3
Range of arccos
For real-valued outputs, arccos returns angles in the interval [0, π] radians, which is the same as [0°, 180°].
How to use this calculator
- Enter a number from -1 to 1.
- Choose radians, degrees, or both.
- Select decimal precision.
- Click Calculate arccos.
You can also press Enter while focused on an input field.
Common arccos values
- arccos(1) = 0 rad = 0°
- arccos(0.5) = π/3 rad = 60°
- arccos(0) = π/2 rad = 90°
- arccos(-0.5) = 2π/3 rad = 120°
- arccos(-1) = π rad = 180°
Why arccos is useful
Arccos appears in geometry, physics, engineering, and computer graphics. For example, it is used to find angles between vectors from a known cosine value. It is also useful when solving triangles and when converting directional data into readable angle measures.
Practical examples
- Finding the angle between two vectors in 2D/3D models.
- Calculating reflection and incidence angles in optics.
- Analyzing rotational movement in robotics.
- Solving right-triangle and unit-circle problems in trigonometry.
Troubleshooting tips
- If you see an error, check that your input is between -1 and 1.
- Remember that JavaScript’s
Math.acos()returns radians by default. - If your result looks rounded too much, increase the decimal precision.
This calculator is designed to be simple, accurate, and fast—ideal for homework checks, quick engineering calculations, and general trigonometry practice.