# Arctan Calculator

Use this arctan calculator to easily calculate the arctan of a given number.

## Arctan function

The arctan 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 to obtain an angle from the tangent trigonometric ratio, which is the ratio between the side opposite to the angle and the adjacent side of the triangle.

The function spans all real numbers (-∞ - +∞) and 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, like 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+x^{2}), which can help you in trigonometry calculations.

## How to calculate the arctan of a number?

The easiest way to calculate it is by using our arctan 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 arctan values:

x | arctan(x) (°) | arctan(x) (rad.) |
---|---|---|

-∞ | -90° | -π/2 |

-√3 | -60° | -π/3 |

-1 | -45° | -π/4 |

-1/√3 | -30° | -π/6 |

0 | 0° | 0 |

1/√3 | 30° | π/6 |

1 | 45° | π/4 |

√3 | 60° | π/3 |

+∞ | 90° | π/2 |

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

## Example of using arctan

Given the figure below of a right angle triangle with known side lengths a = 18 and b = 10, and 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).

#### 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., *"Arctan Calculator"*, [online] Available at: https://www.gigacalculator.com/calculators/arctan-calculator.php URL [Accessed Date: 27 Sep, 2020].