calculator with arccos

Arccos Calculator

Use this calculator to find the inverse cosine (arccos, or cos-1) of a number.

Domain reminder: arccos is only defined for values between -1 and 1.

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?”

Definition: If cos(θ) = x, then arccos(x) = θ (principal value).

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

  1. Enter a number from -1 to 1.
  2. Choose radians, degrees, or both.
  3. Select decimal precision.
  4. 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.

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