Math July 13, 2026 · 8 Min Read

Arccos Calculator – Guide & Formulas

Calculate arccos (inverse cosine) instantly. Enter a cosine value to find the angle in degrees or radians with step-by-step results.

The Arccos Calculator computes the inverse cosine of any value between -1 and 1. Enter a cosine value and instantly receive the angle in both degrees and radians, along with a step-by-step explanation of how the inverse cosine function works.

Key Takeaway

Use the free Arccos Calculator to calculate arccos (inverse cosine) instantly. enter a cosine value to find the angle in degrees or radians with step-by-step results. Get instant results with step-by-step explanations.

How to Use the Arccos Calculator

  1. Enter a cosine value between -1 and 1 in the input field.
  2. The calculator instantly computes the arccos result.
  3. View the angle in both degrees and radians.
  4. Review the step-by-step explanation and formula reference.

The Formula

arccos(x) = θ where cos(θ) = x and 0 ≤ θ ≤ π (or 0° ≤ θ ≤ 180°)

Variable Definitions

  • arccos(x): The angle whose cosine is x, also written as cos⁻¹(x)
  • x: The cosine value (input), must be between -1 and 1
  • θ: The resulting angle in radians (0 to π) or degrees (0° to 180°)
  • cos(θ): The cosine function: adjacent/hypotenuse in a right triangle

Example: Arccos(0.5)

Find the angle whose cosine is 0.5.

  1. Step 1: We need to find θ such that cos(θ) = 0.5.
  2. Step 2: From the unit circle or cosine table, cos(60°) = cos(π/3) = 0.5.
  3. Step 3: Therefore arccos(0.5) = 60° or π/3 radians ≈ 1.0472 radians.
  4. Step 4: Verify: cos(60°) = 0.5 ✓

Frequently Asked Questions

What is arccos?

Arccos (inverse cosine) is the function that takes a cosine value and returns the angle whose cosine is that value. It is written as arccos(x) or cos⁻¹(x) and produces angles between 0° and 180° (0 to π radians).

What is the domain and range of arccos?

The domain of arccos is [-1, 1], meaning the input must be between -1 and 1 inclusive. The range is [0, π] in radians or [0°, 180°] in degrees.

How is arccos different from 1/cos?

Arccos (cos⁻¹) is the inverse function that returns an angle, while 1/cos is the secant function (sec) which returns a ratio. They are completely different operations — do not confuse them.

What is arccos(0)?

arccos(0) = π/2 radians = 90°. This is because cos(90°) = 0. The angle whose cosine is 0 is a right angle.

What is arccos(1)?

arccos(1) = 0 radians = 0°. This is because cos(0°) = 1. The angle whose cosine is 1 is zero radians.

What is arccos(-1)?

arccos(-1) = π radians = 180°. This is because cos(180°) = -1. The angle whose cosine is -1 is a straight angle.

Can arccos return negative angles?

No. By definition, the principal value of arccos always returns angles in the range [0, π] radians or [0°, 180°]. It never returns negative angles.

What are common arccos values?

Common values: arccos(0) = 90°, arccos(0.5) = 60°, arccos(√2/2) = 45°, arccos(√3/2) = 30°, arccos(1) = 0°, arccos(-0.5) = 120°, arccos(-1) = 180°.

How do I convert arccos result from radians to degrees?

Multiply the radian result by 180/π to convert to degrees. For example, arccos(0.5) = π/3 radians × (180/π) = 60°.

What is the relationship between arccos and arcsin?

The identity arccos(x) + arcsin(x) = π/2 (or 90°) relates the two functions. This means the angle whose cosine is x plus the angle whose sine is x always equals 90°.