JavaScript Math.acos(): Arccosine Examples in Radians and Degrees

JavaScript Math.acos() returns the arccosine (inverse cosine) of a number: the angle in radians whose cosine equals the argument. The input must lie in [-1, 1]; outside that range the result is NaN. The output is always in [0, π] radians—convert to degrees when presenting to humans. For the inverse sine, see JavaScript Math.asin(); for angles from x/y pairs prefer JavaScript Math.atan2.

Tested On: The examples were tested with Node.js v20.18.1 on a Linux system. The same Math.acos() behavior works in modern browsers and JavaScript runtimes.

Math.acos Syntax

Math.acos(x)

x must be between -1 and 1. The return value is in radians.

Method 1: Calculate arccosine with Math.acos()

const angle = Math.acos(0.5);

console.log(angle);

Output:

1.0471975511965979

The result is approximately π / 3 radians because the cosine of π / 3 is 0.5.

Method 2: Convert Math.acos Result to Degrees

JavaScript trigonometric functions return radians. Convert radians to degrees by multiplying by 180 / Math.PI.

const radians = Math.acos(0.5);
const degrees = radians * (180 / Math.PI);

console.log(degrees);

Output:

60.00000000000001

The tiny decimal difference is normal floating-point behavior.

Method 3: Handle Values Outside -1 to 1

Math.acos() returns NaN when the input is outside the valid domain.

console.log(Math.acos(2));

Output:

NaN

Validate or clamp input values when they come from user input or floating-point calculations.

Method 4: Find the Angle Between Two Vectors

You can use Math.acos() with the dot product formula to find the angle between vectors.

const a = [1, 0];
const b = [0, 1];

const dot = a[0] * b[0] + a[1] * b[1];
const magnitude = Math.hypot(...a) * Math.hypot(...b);
const degrees = Math.acos(dot / magnitude) * (180 / Math.PI);

console.log(degrees);

Output:

90

The vectors point along the x-axis and y-axis, so the angle between them is 90 degrees.

Common Questions About Math.acos

What is acos in math?

acos is arccosine, the inverse cosine function. It returns the angle whose cosine equals the input value.

Does Math.acos return degrees?

No. Math.acos() returns radians. Convert to degrees with radians * 180 / Math.PI.

Why does Math.acos return NaN?

It returns NaN when the input is less than -1 or greater than 1.

Summary

JavaScript Math.acos() calculates arccosine and returns an angle in radians. Use it for inverse cosine calculations, vector angles, and trigonometry problems where the cosine value is known. The input must be in the range -1 to 1; values outside that domain return NaN. For user-facing math output, convert the radians result to degrees.

Official Documentation

• MDN: Math.acos()