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

Value | ||

Unit | ||

Decimals |

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 to
**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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