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

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#

4545 (degree) is equal to:#

Radian#

UnitSymbolSymbol
(plain text)
Value as symbolicValue as numericNotesUnit conversion formula
radianShow sourceradradradShow 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.2π rad=3602 \pi\ rad = 360^{\circ}Show source......
pi × radianShow sourceπ×rad\pi \times radπ × radShow 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#

UnitSymbolSymbol
(plain text)
Value as symbolicValue as numericNotesUnit conversion formula
degreeShow 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=π180 rad1^{\circ} = \dfrac{\pi}{180}\ radShow source......
minute of arcShow source''Show source...\text{...}-One sixty of degree.1=160=π21600 rad1' = \dfrac{1^{\circ}}{60} = \dfrac{\pi}{21600}\ radShow source......
second of arcShow source''"Show source...\text{...}-One sixty of minute of arc.1"=160=13600=π1296000 rad1" = \dfrac{1'}{60} = \dfrac{1^{\circ}}{3600} = \dfrac{\pi}{1296000}\ radShow source......
third of arcShow source'''Show source...\text{...}-One sixty of second of arc.1=160=13600=1216000=π77760000 rad1''' = \dfrac{1''}{60} = \dfrac{1'}{3600} = \dfrac{1^{\circ}}{216000} = \dfrac{\pi}{77760000}\ radShow source......
fourth of arcShow source''''Show source...\text{...}-One 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}\ radShow source......

Turns and part of turn#

UnitSymbolSymbol
(plain text)
Value as symbolicValue as numericNotesUnit conversion formula
turnShow source--Show source...\text{...}-Equivalent to full angle, i.e. 360 degrees.turn=360=2π rad\text{turn} = 360^{\circ} = 2\pi\ radShow source......
quadrantShow source--Show source...\text{...}-Equivalent to a quarter of a revolution i.e. a right angle.1 quadrant=14 turn=90=π2 rad1\ \text{quadrant} = \dfrac{1}{4}\ \text{turn} = 90^{\circ} = \dfrac{\pi}{2}\ radShow source......
right angleShow source--Show source...\text{...}-Equivalent 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}\ radShow source......
sextantShow source--Show source...\text{...}-Equivalent 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}\ radShow source......
octantShow source--Show source...\text{...}-Equivalent 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}\ radShow source......
signShow source--Show source...\text{...}-Equivalent 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}\ radShow 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 hour=124 turn=15=π12 rad1\ \text{hour} = \dfrac{1}{24}\ \text{turn} = 15^{\circ} = \dfrac{\pi}{12}\ radShow source......
pointShow source--Show source...\text{...}-Equivalent 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}\ radShow source......
minute angle (1/60 of turn)Show source--Show source...\text{...}-Equivalent 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}\ radShow source......

military#

UnitSymbolSymbol
(plain text)
Value as symbolicValue as numericNotesUnit conversion formula
milliradianShow sourcemilmilmilShow 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=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.
Show source......
milliradian (NATO)Show sourcemilmilmilShow 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 milNATO=3606400=π3200 rad1\ mil_{NATO} = \dfrac{360^{\circ}}{6400} = \dfrac{\pi}{3200}\ radShow source......
milliradian (Soviet Union)Show sourcemilmilmilShow 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 milSov.=3606000=π3000 rad1\ mil_{Sov.} = \dfrac{360^{\circ}}{6000} = \dfrac{\pi}{3000}\ radShow source......
milliradian (Sweden)Show sourcemilmilmilShow 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 milSweden=3606300=π3150 rad1\ mil_{Sweden} = \dfrac{360^{\circ}}{6300} = \dfrac{\pi}{3150}\ radShow source......

other#

UnitSymbolSymbol
(plain text)
Value as symbolicValue as numericNotesUnit conversion formula
grad; gradian; gonShow sourcegradgradgradShow 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=90100=π2001\ 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).
  • 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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