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#

$45$ (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) 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 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.

Tags and links to this website#

Tags:

angle · angular_measure_units_converter

Tags to Polish version:

kat · konwerter_jednostek_miary_kata

What tags this calculator has#

CONVERTER · UNITS · A -> Z (all)

Permalink#

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https://calculla.com/angle?inUnitId=deg&inValue=$symbolic(45)&inPrecision=9

Links to external sites (leaving Calculla?)#

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