Arccos Calculator

The arccos calculator returns the angle whose cosine equals your input, for any value between -1 and 1. It is the inverse of cosine, written cos⁻¹(x) or acos(x). Pick degrees, radians, gradians, or turns from the unit selector on the angle field, and the result updates as you type.

What is arccos?

If $\cos(\theta) = x \implies \arccos(x) = \theta$. The complication is that cosine is not one-to-one, it repeats every 360°, so the inverse has to pick a single branch. Arccos returns the angle in the range 0 to π radians (0° to 180°), called the principal value. Anything outside [-1, 1] has no real answer, because cosine never goes past ±1.

How to use the calculator

Type into either field. Give x and you get back the angle; give the angle and you get back x. Switch units on the angle field whenever you want, and the value reconverts.

Where does arccos show up

In geometry, arccos turns the law of cosines into an angle finder once you know all three sides of a triangle. Physics uses it to pull phase angles out of wave amplitudes, and to recover the angle between two vectors from their dot product. Graphics and game code lean on the same vector-angle trick for lighting and camera math.

A few things worth knowing

• arccos rejects anything outside [-1, 1]. If you are feeding it a ratio, clamp first or check for floating-point rounding.

• The output sits between 0° and 180° (0 and π radians). To recover an angle in the other quadrant, subtract from 360° or negate it.

• Use degrees for engineering and everyday work, radians for calculus. The unit switch handles the conversion.

• Three values worth memorizing: arccos(1) = 0°, arccos(0) = 90°, arccos(-1) = 180°.

Frequently asked questions

What is the domain of arccos?

[-1, 1]. Cosine never produces a value outside that range, so the inverse cannot accept one either. Inputs like 1.0000001 from floating-point rounding will throw, so clamp before you call it.

Is cos⁻¹(x) the same as 1/cos(x)?

Different things, and the notation collision causes a lot of grief in intro trig. cos⁻¹(x) is the inverse function (arccos). The reciprocal 1/cos(x) is the secant, sec(x).