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

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

 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) 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 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).
• 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 measurein degrees angular measurein 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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