# Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

# Inputs data - value and unit, which we're going to convert#

Value | ||

Unit | ||

Decimals |

# Image: how your angle looks like#

# $45$ (degree) is equal to:#

# Radian#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

radian | Show source$rad$ | rad | Show source$\text{...}$ | - | The basic measurement of plane angle unit used in mathematics, physics and technical sciences. The full angle corresponds to 2π radians, or 360 degrees.$2 \pi\ rad = 360^{\circ}$ | Show source$...$ |

pi × radian | Show source$\pi \times rad$ | π × rad | Show source$\text{...}$ | - | The helper unit created by multiplying one radian by the number π. Unit used to simplify calculations. Full turnover in units defined in this way is 2. | Show source$...$ |

# Degree#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

degree | Show source$^\circ$ | ° | Show source$\text{...}$ | - | One of the most popular measurement of plane angle unit. Full rotation corresponds to 360 degrees, or 2π radians.$1^{\circ} = \dfrac{\pi}{180}\ rad$ | Show source$...$ |

minute of arc | Show source$'$ | ' | Show source$\text{...}$ | - | One sixty of degree.$1' = \dfrac{1^{\circ}}{60} = \dfrac{\pi}{21600}\ rad$ | Show source$...$ |

second of arc | Show source$''$ | " | Show source$\text{...}$ | - | One sixty of minute of arc.$1" = \dfrac{1'}{60} = \dfrac{1^{\circ}}{3600} = \dfrac{\pi}{1296000}\ rad$ | Show source$...$ |

third of arc | Show source$'''$ | ‴ | Show source$\text{...}$ | - | One sixty of second of arc.$1''' = \dfrac{1''}{60} = \dfrac{1'}{3600} = \dfrac{1^{\circ}}{216000} = \dfrac{\pi}{77760000}\ rad$ | Show source$...$ |

fourth of arc | Show source$''''$ | ⁗ | Show source$\text{...}$ | - | One sixty of third of arc.$1'''' = \dfrac{1'''}{60} = \dfrac{1''}{3600} = \dfrac{1'}{216000} = \dfrac{1^{\circ}}{12960000} = \dfrac{\pi}{4665600000}\ rad$ | Show source$...$ |

# Turns and part of turn#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

turn | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to full angle, i.e. 360 degrees.$\text{turn} = 360^{\circ} = 2\pi\ rad$ | Show source$...$ |

quadrant | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to a quarter of a revolution i.e. a right angle.$1\ \text{quadrant} = \dfrac{1}{4}\ \text{turn} = 90^{\circ} = \dfrac{\pi}{2}\ rad$ | Show source$...$ |

right angle | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to a quarter turn i.e. 90 degrees.$\text{right angle} = \dfrac{1}{4}\ \text{turn} = 90^{\circ} = \dfrac{\pi}{2}\ rad$ | Show source$...$ |

sextant | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to one sixth of a turn i.e. 60 degrees.$1\ \text{sextant} = \dfrac{1}{6}\ \text{turn} = 60^{\circ} = \dfrac{\pi}{3}\ rad$ | Show source$...$ |

octant | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to one-eighth of a turn i.e. 45 degrees.$1\ \text{octant} = \dfrac{1}{8}\ \text{turn} = 45^{\circ} = \dfrac{\pi}{4}\ rad$ | Show source$...$ |

sign | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to one twelfth of a turn i.e. 30 degrees.$1\ \text{sign} = \dfrac{1}{12}\ \text{turn} = 30^{\circ} = \dfrac{\pi}{6}\ rad$ | Show source$...$ |

hour angle (1/24 of turn) | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to one-twenty-fourth of a turn i.e. 15 degrees.$1\ \text{hour} = \dfrac{1}{24}\ \text{turn} = 15^{\circ} = \dfrac{\pi}{12}\ rad$ | Show source$...$ |

point | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to one-thirty-second of a turn i.e. 11.25 degrees.$1\ \text{point} = \dfrac{1}{32}\ \text{turn} = 11.25^{\circ} = \dfrac{\pi}{16}\ rad$ | Show source$...$ |

minute angle (1/60 of turn) | Show source$-$ | - | Show source$\text{...}$ | - | Equivalent to one sixtieth of a turn i.e. 6 degrees.$1\ \text{minute} = \dfrac{1}{60}\ \text{turn} = 6^{\circ} = \dfrac{\pi}{30}\ rad$ | Show source$...$ |

# military#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

milliradian | Show source$mil$ | mil | Show source$\text{...}$ | - | Unit of measure of angle used in the army. Milliradian (mrad, mil) is the angle at which you can see a curve of one meter from a distance of one kilometer. One milliradian corresponds to one thousandth of a radian, or approximately 1/6283.2 of a turn. $1 \ mil = \dfrac{1}{1000}\ rad = \dfrac{180^{\circ}}{1000 \pi} \approx \dfrac{360^{\circ}}{6283.2}$ In practice, military applications usually use approximated units, e.g.: - 1/6400 of a turn (→ see the milliradian NATO),
- 1/6000 of a turn (→ see the Soviet milliradian),
- 1/6300 of a turn (→ see the Swedish milliradian)
| Show source$...$ |

milliradian (NATO) | Show source$mil$ | mil | Show source$\text{...}$ | - | A unit of measure of angle that is an approximation of the real milliradian used by NATO forces. One NATO milliradian corresponds to 1/6400 of a turn. Check out real milliradian unit to learn more.$1\ mil_{NATO} = \dfrac{360^{\circ}}{6400} = \dfrac{\pi}{3200}\ rad$ | Show source$...$ |

milliradian (Soviet Union) | Show source$mil$ | mil | Show source$\text{...}$ | - | A measure of angle that is an approximation of the real milliradian used in the army of the former Soviet Union. One Soviet milliradian corresponds to 1/6000 of a turn. Check out real milliradian unit to learn more.$1\ mil_{Sov.} = \dfrac{360^{\circ}}{6000} = \dfrac{\pi}{3000}\ rad$ | Show source$...$ |

milliradian (Sweden) | Show source$mil$ | mil | Show source$\text{...}$ | - | A unit of angle measurement that is an approximation of the real milliradian used, among others, in Sweden and Finland. One Swedish milliradian corresponds to 1/6300 of a turn. Sometimes also called streck. Check out real milliradian unit to learn more.$1\ mil_{Sweden} = \dfrac{360^{\circ}}{6300} = \dfrac{\pi}{3150}\ rad$ | Show source$...$ |

# other#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

grad; gradian; gon | Show source$grad$ | grad | Show source$\text{...}$ | - | A measure for angle unit used in geodesy. One grad (gon, gradus) corresponds to 1/100 of a right angle i.e. 9/10 of a degree.$1\ grad = \dfrac{90^{\circ}}{100} = \dfrac{\pi}{200}$ | Show source$...$ |

# Some facts#

- 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.

# Angles classification

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 |

# How to convert#

**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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# Ancient version of this site - links#

In 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.

Direct link to the old version: "Calculla v1" version of this calculator

Direct link to the old version: "Calculla v1" version of this calculator