Arccos Calculator

Use this calculator to easily calculate the arccos of a number.

Calculation results

arccos(0.5) = 60 degrees
arccos(0.5) = 1.047198 radians
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Arccos function

The arccos (arcus cosine, arccosine) is one of the inverse trigonometric functions (antitrigonometric functions, arcus functions) and is the inverse of the cosine function. It is sometimes written as cos-1(x), but this notation should be avoided as it can be confused with an exponent notation (power of, raised to the power of). The arccos is used to obtain an angle from the cosine trigonometric ratio, which is the ratio between the side adjacent to the angle and the hypotenuse in a right triangle.

The function spans from -1 to 1, and so do the results from our arccos calculator. The range of the angle values is usually between 0° and 180°. There are a number of arccos rules, like that cos(arccos(x)) = x, or that arccosα + arccosβ = arccos(αβ - √((1-α2)(1-β2)), as well as sine of the arccosine: sin(arccos(x)) = √(1-x2), which can help you in trigonometry calculus.

How to calculate the arccosine of a number?

The easiest way to calculate it is by using our arccos calculator above, which will output results in both degrees and radians. Other ways include other given information, such as the values of other trigonometric functions for the same angle or other angles in the same triangle.

Here is a table of common arccos values:

Common values of the arccos function
xarccos(x) (°)arccos(x) (rad.)
-1 180° π
-√3 / 2 150° 5π/6
-√2 / 2 135° 3π/4
-1/2 120° 2π/3
0 90° π/2
1/2 60° π/3
√2 / 2 45° π/4
√3 / 2 30° π/5
1 π/6

π is, of course, the mathematical constant about equal to 3.14159.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:
Georgiev G.Z., "Arccos Calculator", [online] Available at: https://www.gigacalculator.com/calculators/arccos-calculator.php URL [Accessed Date: 23 Jul, 2019].