Arccosine (arccos or cos⁻¹) is the inverse of the cosine function. Given a value x, arccos(x) returns the angle θ such that cos(θ) = x. The output angle lies in the range [0°, 180°] (or [0, π] radians).

Why must the input be between -1 and 1?

The cosine of any angle always produces a value in [-1, 1]. Therefore the inverse operation is only defined for inputs in that range. Values outside it have no real-number solution.

How do I convert the result from radians to degrees?

Multiply the radian value by 180/π (approximately 57.2958). The calculator does this automatically and shows both units side by side.

What is the difference between arccos and cos⁻¹?

They are the same function. "cos⁻¹" is the notation used on most calculators, while "arccos" is the conventional mathematical notation. Both mean the inverse cosine.

How does arccos differ from arcsin?

Both take inputs in [-1, 1], but their output ranges differ. Arcsin returns angles in [-90°, 90°], while arccos returns angles in [0°, 180°]. They are complementary: arcsin(x) + arccos(x) = 90°.

Can arccos return an angle greater than 180 degrees?

No. By definition the principal value of arccos is restricted to [0°, 180°]. If your problem requires an angle in a different range, you must apply the appropriate supplementary or reflex angle identity manually.

Arccosine Calculator

Enter a value between -1 and 1 to instantly get its arccosine in both degrees and radians.

Input Value

Value (must be between −1 and 1)

Common values

Result

Enter a value and press Calculate.

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Summary

The Arccosine Calculator computes the inverse cosine (arccos) of any number in the domain [-1, 1]. It instantly returns the angle in both degrees and radians, making it useful for trigonometry, physics, and engineering calculations. All computation happens in your browser using the JavaScript Math.acos function.

How it works

Enter a numeric value between -1 and 1 in the input field.
The calculator checks that the value is within the valid domain for arccos.
Math.acos() computes the result in radians (range: 0 to π).
The radian result is converted to degrees by multiplying by 180/π.
Both results are displayed immediately with up to 8 significant figures.

Use cases

Find the angle whose cosine equals a known ratio in a right triangle.
Convert a cosine value back to its source angle in physics problems.
Solve for angles in engineering and structural calculations.
Verify trigonometric identities and homework answers.
Compute direction or inclination angles from a horizontal/hypotenuse ratio.
Use as a quick reference in scientific or graphing calculator workflows.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu