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

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

Value
Unit
Decimals

#

Radian#

UnitSymbolSymbol
(plain text)
ValueNotes
radianShow sourceradradrad0.785398163The basic measurement of plane angle unit used in mathematics, physics and technical sciences. The full angle corresponds to 2π radians, or 360 degrees.2π rad=3602 \pi\ rad = 360^{\circ}
pi × radianShow sourceπ×rad\pi \times radπ × rad0.25The 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#

UnitSymbolSymbol
(plain text)
ValueNotes
degreeShow source^\circ°45One of the most popular measurement of plane angle unit. Full rotation corresponds to 360 degrees, or 2π radians.1=π180 rad1^{\circ} = \dfrac{\pi}{180}\ rad
minute of arcShow source''2700One sixty of degree.1=160=π21600 rad1' = \dfrac{1^{\circ}}{60} = \dfrac{\pi}{21600}\ rad
second of arcShow source''"162000One sixty of minute of arc.1"=160=13600=π1296000 rad1" = \dfrac{1'}{60} = \dfrac{1^{\circ}}{3600} = \dfrac{\pi}{1296000}\ rad
third of arcShow source'''9720000One sixty of second of arc.1=160=13600=1216000=π77760000 rad1''' = \dfrac{1''}{60} = \dfrac{1'}{3600} = \dfrac{1^{\circ}}{216000} = \dfrac{\pi}{77760000}\ rad
fourth of arcShow source''''583200000One sixty of third of arc.1=160=13600=1216000=112960000=π4665600000 rad1'''' = \dfrac{1'''}{60} = \dfrac{1''}{3600} = \dfrac{1'}{216000} = \dfrac{1^{\circ}}{12960000} = \dfrac{\pi}{4665600000}\ rad

Turns and part of turn#

UnitSymbolSymbol
(plain text)
ValueNotes
turnShow source--0.125Equivalent to full angle, i.e. 360 degrees.turn=360=2π rad\text{turn} = 360^{\circ} = 2\pi\ rad
quadrantShow source--0.5Equivalent to a quarter of a revolution i.e. a right angle.1 kwadrant=14 turn=90=π2 rad1\ \text{kwadrant} = \dfrac{1}{4}\ \text{turn} = 90^{\circ} = \dfrac{\pi}{2}\ rad
right angleShow source--0.5Equivalent to a quarter turn i.e. 90 degrees.right angle=14 turn=90=π2 rad\text{right angle} = \dfrac{1}{4}\ \text{turn} = 90^{\circ} = \dfrac{\pi}{2}\ rad
sextantShow source--0.75Equivalent to one sixth of a turn i.e. 60 degrees.1 sextant=16 turn=60=π3 rad1\ \text{sextant} = \dfrac{1}{6}\ \text{turn} = 60^{\circ} = \dfrac{\pi}{3}\ rad
octantShow source--1Equivalent to one-eighth of a turn i.e. 45 degrees.1 octant=18 turn=45=π4 rad1\ \text{octant} = \dfrac{1}{8}\ \text{turn} = 45^{\circ} = \dfrac{\pi}{4}\ rad
signShow source--1.5Equivalent to one twelfth of a turn i.e. 30 degrees.1 sign=112 turn=30=π6 rad1\ \text{sign} = \dfrac{1}{12}\ \text{turn} = 30^{\circ} = \dfrac{\pi}{6}\ rad
hour angle (1/24 of turn)Show source--3Equivalent to one-twenty-fourth of a turn i.e. 15 degrees.1 hour=124 turn=15=π12 rad1\ \text{hour} = \dfrac{1}{24}\ \text{turn} = 15^{\circ} = \dfrac{\pi}{12}\ rad
pointShow source--4Equivalent to one-thirty-second of a turn i.e. 11.25 degrees.1 point=132 turn=11.25=π16 rad1\ \text{point} = \dfrac{1}{32}\ \text{turn} = 11.25^{\circ} = \dfrac{\pi}{16}\ rad
minute angle (1/60 of turn)Show source--7.5Equivalent to one sixtieth of a turn i.e. 6 degrees.1 minute=160 turn=6=π30 rad1\ \text{minute} = \dfrac{1}{60}\ \text{turn} = 6^{\circ} = \dfrac{\pi}{30}\ rad

military#

UnitSymbolSymbol
(plain text)
ValueNotes
milliradianShow sourcemilmilmil785.398163397Unit 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=11000 rad=1801000π3606283.21 \ 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)
Sometimes, to emphasize the theoretical nature of a unit being exactly one thousandth of a radian, the term real milliradian is used.
milliradian (NATO)Show sourcemilmilmil800A 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 milNATO=3606400=π3200 rad1\ mil_{NATO} = \dfrac{360^{\circ}}{6400} = \dfrac{\pi}{3200}\ rad
milliradian (Soviet Union)Show sourcemilmilmil750A 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 milSov.=3606000=π3000 rad1\ mil_{Sov.} = \dfrac{360^{\circ}}{6000} = \dfrac{\pi}{3000}\ rad
milliradian (Sweden)Show sourcemilmilmil787.5A 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 milSweden=3606300=π3150 rad1\ mil_{Sweden} = \dfrac{360^{\circ}}{6300} = \dfrac{\pi}{3150}\ rad

other#

UnitSymbolSymbol
(plain text)
ValueNotes
grad; gradian; gonShow sourcegradgradgrad50A 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=90100=π2001\ grad = \dfrac{90^{\circ}}{100} = \dfrac{\pi}{200}

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).
  • 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 nameangular measure
in degrees
angular measure
in radians
zero angle0
half-whole angle180°π
whole angle360°
right angle90°π/2
acute anglefrom 0° to 90°from 0 to π/2
obtuse anglefrom 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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