Inputs data  value and unit, which we're going to convert#
Value  
Unit  
Decimals 
Radian#
Unit  Symbol  Symbol (plain text)  Value  Notes 
radian  Show source$rad$  rad  0.785398163  The basic measurement of plane angle unit used in mathematics, physics and technical sciences. The full angle corresponds to 2π radians, or 360 degrees.$2 \pi\ rad = 360^{\circ}$ 
pi × radian  Show source$\pi \times rad$  π × rad  0.25  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. 
Degree#
Unit  Symbol  Symbol (plain text)  Value  Notes 
degree  Show source$^\circ$  °  45  One of the most popular measurement of plane angle unit. Full rotation corresponds to 360 degrees, or 2π radians.$1^{\circ} = \dfrac{\pi}{180}\ rad$ 
minute of arc  Show source$'$  '  2700  One sixty of degree.$1' = \dfrac{1^{\circ}}{60} = \dfrac{\pi}{21600}\ rad$ 
second of arc  Show source$''$  "  162000  One sixty of minute of arc.$1" = \dfrac{1'}{60} = \dfrac{1^{\circ}}{3600} = \dfrac{\pi}{1296000}\ rad$ 
third of arc  Show source$'''$  ‴  9720000  One sixty of second of arc.$1''' = \dfrac{1''}{60} = \dfrac{1'}{3600} = \dfrac{1^{\circ}}{216000} = \dfrac{\pi}{77760000}\ rad$ 
fourth of arc  Show source$''''$  ⁗  583200000  One sixty of third of arc.$1'''' = \dfrac{1'''}{60} = \dfrac{1''}{3600} = \dfrac{1'}{216000} = \dfrac{1^{\circ}}{12960000} = \dfrac{\pi}{4665600000}\ rad$ 
Turns and part of turn#
Unit  Symbol  Symbol (plain text)  Value  Notes 
turn  Show source$$    0.125  Equivalent to full angle, i.e. 360 degrees.$\text{turn} = 360^{\circ} = 2\pi\ rad$ 
quadrant  Show source$$    0.5  Equivalent to a quarter of a revolution i.e. a right angle.$1\ \text{kwadrant} = \dfrac{1}{4}\ \text{turn} = 90^{\circ} = \dfrac{\pi}{2}\ rad$ 
right angle  Show source$$    0.5  Equivalent to a quarter turn i.e. 90 degrees.$\text{right angle} = \dfrac{1}{4}\ \text{turn} = 90^{\circ} = \dfrac{\pi}{2}\ rad$ 
sextant  Show source$$    0.75  Equivalent to one sixth of a turn i.e. 60 degrees.$1\ \text{sextant} = \dfrac{1}{6}\ \text{turn} = 60^{\circ} = \dfrac{\pi}{3}\ rad$ 
octant  Show source$$    1  Equivalent to oneeighth of a turn i.e. 45 degrees.$1\ \text{octant} = \dfrac{1}{8}\ \text{turn} = 45^{\circ} = \dfrac{\pi}{4}\ rad$ 
sign  Show source$$    1.5  Equivalent to one twelfth of a turn i.e. 30 degrees.$1\ \text{sign} = \dfrac{1}{12}\ \text{turn} = 30^{\circ} = \dfrac{\pi}{6}\ rad$ 
hour angle (1/24 of turn)  Show source$$    3  Equivalent to onetwentyfourth of a turn i.e. 15 degrees.$1\ \text{hour} = \dfrac{1}{24}\ \text{turn} = 15^{\circ} = \dfrac{\pi}{12}\ rad$ 
point  Show source$$    4  Equivalent to onethirtysecond of a turn i.e. 11.25 degrees.$1\ \text{point} = \dfrac{1}{32}\ \text{turn} = 11.25^{\circ} = \dfrac{\pi}{16}\ rad$ 
minute angle (1/60 of turn)  Show source$$    7.5  Equivalent to one sixtieth of a turn i.e. 6 degrees.$1\ \text{minute} = \dfrac{1}{60}\ \text{turn} = 6^{\circ} = \dfrac{\pi}{30}\ rad$ 
military#
Unit  Symbol  Symbol (plain text)  Value  Notes 
milliradian  Show source$mil$  mil  785.398163397  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.:

milliradian (NATO)  Show source$mil$  mil  800  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.$1\ mil_{NATO} = \dfrac{360^{\circ}}{6400} = \dfrac{\pi}{3200}\ rad$ 
milliradian (Soviet Union)  Show source$mil$  mil  750  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.$1\ mil_{Sov.} = \dfrac{360^{\circ}}{6000} = \dfrac{\pi}{3000}\ rad$ 
milliradian (Sweden)  Show source$mil$  mil  787.5  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.$1\ mil_{Sweden} = \dfrac{360^{\circ}}{6300} = \dfrac{\pi}{3150}\ rad$ 
other#
Unit  Symbol  Symbol (plain text)  Value  Notes 
grad; gradian; gon  Show source$grad$  grad  50  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.$1\ grad = \dfrac{90^{\circ}}{100} = \dfrac{\pi}{200}$ 
Some facts#
 The angle is part of the plane bounded by two halflines having a common origin.
 The halflines 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 threedimensional 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 (breng: trapezium, useng: 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.
 Inscribed angle – when its vertex is localized on boundaries of circle.
Angles classification
angle name  angular measure in degrees  angular measure in radians 
zero angle  0°  0 
halfwhole 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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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