# Arctan Calculator

The Online arctan(x) calculator, also known as an inverse tangent calculator, is a convenient tool for finding the arctangent or inverse tangent of a given value. By entering a numerical value into the calculator, you can obtain the angle in radians or degrees corresponding to that value.

## What is Arctangent

Arctangent, also known as inverse tangent, is a mathematical function that yields the angle whose tangent is a given number or ratio. It is the inverse of the tangent function. The arctangent function is denoted as arctan(x) or atan(x), where x is the input value. For example, if you have a value of 0.577 and you want to find the corresponding angle, you would use the arctangent function. It will return the angle (in radians or degrees) whose tangent is approximately 0.577. The arctangent function is widely used in various fields such as mathematics, physics, computer science, and engineering, particularly in solving problems related to angles, triangles, and trigonometry.

## Arctangent definition

The arctangent function is the inverse function of y = tan(x).

arctan(*y*) = tan^{-1}(*y*) = *x*+ *kπ*

For every

*k *= {...,-2,-1,0,1,2,...}

For example, If the tangent of 45° is 1:

tan(45°) = 1

Then the arctangent of 1 is 45°:

arctan(1) = tan^{-1}(1) = 45°

## Arctangent table

y | x = arctan(y) | |
---|---|---|

degrees | radians | |

-1.732050808 | -60° | -π/3 |

-1 | -45° | -π/4 |

-0.577350269 | -30° | -π/6 |

0 | 0° | 0 |

0.577350269 | 30° | π/6 |

1 | 45° | π/4 |

1.732050808 | 60° | π/3 |

## Arctan Calculator Example

Input (Tangent Value) | Output (Arctan Value) |
---|---|

0 | 0 radians / 0 degrees |

1 | 0.7854 radians / 45 degrees |

-1 | -0.7854 radians / -45 degrees |

0.5 | 0.4636 radians / 26.565 degrees |

-0.5 | -0.4636 radians / -26.565 degrees |

2 | 1.1071 radians / 63.435 degrees |

-2 | -1.1071 radians / -63.435 degrees |

In this example, you can input different values for the tangent and obtain the corresponding arctan values in both radians and degrees. This table provides a clear visualization of how the arctan function calculates the angles based on the given tangent values.

Please note that the values in the table are rounded to four decimal places for simplicity. Depending on your specific calculator or programming application, you may get more precise results.