Use this arctan calculator to lớn easily calculate the arctan of a given number. Online arctangent calculation tool to lớn compute the arcus tangens function in degrees or radians. Supports input đầu vào of decimal numbers (0.5, 6, -1, etc.) & fractions (1/3, 3/4, 1/6, -4/3 etc.).

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## Arctan function

The arctan (a.k.a. arcus tangens) is one of the inverse trigonometric functions (antitrigonometric functions) and is the inverse of the tangent function. It is sometimes written as tan-1(x), but this notation should be avoided as it can cause confusion with an exponent notation. The arctan is used lớn obtain an angle from the tangent trigonometric ratio, which is the ratio between the side opposite khổng lồ the angle and the adjacent side of the triangle.

The function spans all real numbers (-∞ - +∞) & so do the results from our calculator. The range of the angle values is usually between -90° and 90°. There are a number of arctan rules, lượt thích that tan(arctan(x)) = x, or that arctanα + arctanβ = arctan((α + β) / (1-αβ)), as well as sine of the arctangent: sin(arctan(x)) = x / √(1+x2), which can help you in trigonometry calculations.

## How to calculate the arctan of a number?

The easiest way khổng lồ calculate it is by using our arctan calculator above, which will output results in both degrees và radians. Other ways require additional information lớn have been provided such as the values of other trigonometric functions for the same angle or for other angles in a triangle (see example below).

Here is a table of common arctan values:

Common values of the arctan functionxarctan(x) (°)arctan(x) (rad.)
-∞-90°-π/2
-√3-60°-π/3
-1-45°-π/4
-1/√3-30°-π/6
00
1/√330°π/6
145°π/4
√360°π/3
+∞90°π/2

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

## Example of using arctan

Given the figure below of a right angle triangle with known side lengths a = 18 & b = 10, & a right angle at point C, how can we find the angle β at point B using the inverse tangent function? Knowing that the tangent of β equals the opposite side divided by the adjacent side, one gets tan(β) = b / a = 10 / 18 = 0.555. Then simply use the inverse function to get β = arctan(0.555) = 29.03° (or 0.507 in radians).

## Calculating arctangent of a fraction

Oftentimes the tangent value will be given or calculated as a simple fraction, e.g. 3/4. While one can use a fraction to lớn decimal converter to convert the fraction into a decimal, our arctangent calculator actually supports direct input đầu vào of various fractions lượt thích 1/2, 1/3, 1/6, 3/4, 4/3, -2/3, và even 0.3/.5 . Lớn compute arctan(3/4) or arctan(4/3) or another x/y fraction, simply enter it into the input đầu vào field và press "calculate".

For convenience, here is a table of common arctangent values of fraction tangents:

Common arc tung values of fraction tangentsx/yarctan(x/y) (°)arctan(x/y) (rad.)