What is the arccos (inverse cosine) of a value?

The arccos of a value x is the angle whose cosine is x. It returns the principal angle in the range [0, π] radians (or [0°, 180°]). For example, arccos(0.5) = π/3 radians or 60°.

What values can I enter for the cosine value?

The cosine value must be between -1 and 1 inclusive. If you enter a number outside this range, the arccos is undefined because cosine values never exceed 1 in magnitude.

Why does the calculator show results in both radians and degrees?

Radians and degrees are two common units for measuring angles. The calculator provides both so you can use the result directly in your work without manual conversion. For example, arccos(-1) = π radians = 180°.

Math

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Arccos Calculator.

Calculate the principal inverse cosine in radians and degrees.

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02 / ANSWER

Cosine value

Angle (rad)

1.047198rad

Angle

60°

Results update automatically as you type.

Use Cases

Solve trigonometry problems

Find the angle when you know the cosine ratio, useful in geometry, physics, and engineering calculations.

Example: If cos(θ) = 0.7071, then θ = arccos(0.7071) ≈ 45°.

Convert between radians and degrees

Get the angle in both units simultaneously, saving time when you need to switch between them.

Example: arccos(0) gives 90° or π/2 radians.

Frequently Asked Questions

What is the arccos (inverse cosine) of a value?: The arccos of a value x is the angle whose cosine is x. It returns the principal angle in the range [0, π] radians (or [0°, 180°]). For example, arccos(0.5) = π/3 radians or 60°.
What values can I enter for the cosine value?: The cosine value must be between -1 and 1 inclusive. If you enter a number outside this range, the arccos is undefined because cosine values never exceed 1 in magnitude.
Why does the calculator show results in both radians and degrees?: Radians and degrees are two common units for measuring angles. The calculator provides both so you can use the result directly in your work without manual conversion. For example, arccos(-1) = π radians = 180°.

Tips & Common Mistakes

Tips

Ensure your input is between -1 and 1. Values outside this range will not produce a real result.
Remember that arccos returns the principal value, which is always between 0 and π (or 0° and 180°).
Use the result in radians for calculus or physics, and degrees for everyday geometry or navigation.
Double-check your input: a small error in the cosine value can lead to a significant angle difference.

Common Mistakes to Avoid

Entering a value greater than 1 or less than -1, which is invalid for arccos.
Confusing arccos with the reciprocal of cosine (secant). Arccos is the inverse function, not 1/cos.
Forgetting that the result is limited to the principal range, so you might need to add multiples of 2π for other solutions.

Last updated: August 13, 2026