Angle units converter. Converts radians, degrees, turns and many more.

Unit | Symbol | Symbol (plain text) | Value |

radian | Show source$rad$ | rad | 0.785398163 |

pi × radian | Show source$\pi \times rad$ | π × rad | 0.25 |

Unit | Symbol | Symbol (plain text) | Value |

degree | Show source$^\circ$ | ° | 45 |

minute of arc | Show source$'$ | ' | 2700 |

second of arc | Show source$"$ | " | 162000 |

Unit | Symbol | Symbol (plain text) | Value |

turn | Show source$$ | 0.125 | |

quadrant | Show source$$ | 0.5 | |

right angle | Show source$$ | 0.5 | |

sextant | Show source$$ | 0.75 | |

octant | Show source$$ | 1 | |

sign | Show source$$ | 1.5 | |

hour angle (1/24 of turn) | Show source$$ | 3 | |

point | Show source$$ | 4 | |

minute angle (1/60 of turn) | Show source$$ | 7.5 |

Unit | Symbol | Symbol (plain text) | Value |

grad; gradian; gon | Show source$$ | 50 | |

mil | Show source$$ | 785.375 | |

mil NATO | Show source$$ | 800 | |

mil Soviet | Show source$$ | 750 | |

mil Sweden (streck) | Show source$$ | 787.5 |

- The angle is part of the plane bounded by two half-lines having a common origin.
- The half-lines forming an angle are called the
**arms**, and the point in which the arms are in contact is called the**vertex**. - In everyday language, we often say "angle", when we think the
**angular measure**. - Angles are used to give location of object on the map. Point on the map is localized by two angles (coordinates):
**latitude**and**longitude**. The reason of this, is fact, that the Earth is roughly spherical shape. - In everyday life, most common angle units are degrees. In cartography, minutes (1/60 of degree) and - in case of more detailed measurements - seconds (1/60 of minute) are useful. Mathematicians and physicists use mainly radians.
- The concept of angle is stricly related with
**trigonometric functions**, which have angle argument. Example trigonometric functions are**sinus**(sin),**cosinus**(cos) or**tangens**(tg). - There are more general concepts of angle expanding definition to 3D space or even to spaces with more than three dimensions. The equivalent of plane angle in three-dimensional space is
**solid angle**. - If we sort arms of the angle, in such a way that one arm will be considered first and the second one final, then we will call such angle -
**directed angle**. The directed angle can be defined by pair of two vectors with common origin {**u**,**v**}. - There are many interesting angle related properties:

- The sum of all angles in triangle is 180 degrees (π).

- The sum of all angles in any quadrilateral (so in rectangle or square too) is 360 degrees (2π).

- In trapezium (br-eng: trapezium, us-eng: trapezoid) the sum of the neighbouring angles next to both short and long basis is 180 degrees (π).

- The sum of all angles in triangle is 180 degrees (π).
- Circle can contains two kinds of angles:

**Inscribed angle**– when its vertex is localized on boundaries of circle.

**Central angle**– when its vertex is localized in the center of circle.

angle name | angular measure in degrees | angular measure in radians |

zero angle | 0° | 0 |

half-whole angle | 180° | π |

whole angle | 360° | 2π |

right angle | 90° | π/2 |

acute angle | from 0° to 90° | from 0 to π/2 |

obtuse angle | from 90° to 180° | from π/2 to π |

**Enter the number to field "value"**- enter the NUMBER only, no other words, symbols or unit names. You can use dot (**.**) or comma (**,**) to enter fractions.

Examples:- 1000000
- 123,23
- 999.99999

**Find and select your starting unit in field "unit"**. Some unit calculators have huge number of different units to select from - it's just how complicated our world is...**And... you got the result**in the table below. You'll find several results for many different units - we show you all results we know at once. Just find the one you're looking for.

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"Calculla v1" version of this calculatorIn December 2016 the Calculla website has been republished using new technologies and all calculators have been rewritten. Old version of the Calculla is still available through this link: v1.calculla.com. We left the version 1 of Calculla untouched for archival purposes.

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