Angle Unit Converter
To use this angle converter, choose two units, then type some value in the box at left (input). The converted result will immediately appear in the output box at right.
Angle Unit Converter 

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About Angles
Definition: A shape, formed by two lines or rays diverging from a common point (the vertex).
The angular measure of an object is usually expressed in degrees, arcminutes or arcseconds. Just as an hour is divided into 60 minutes and a minute into 60 seconds, a degree is divided into 60 arcminutes and an arcminute is divided into 60 arcseconds.
Angular Measurements and Units
To make basic angle measurements, we can use a protractor which is probabily the most basic anglemeasuring instrument, a common object used in school math classes.
To make precision angle measurements we need a beter instrument like a Digital AngleMeasuring Device, a Theodolite  used mainly by surveyors in civil engineering roles  or a Goniometer.
How small is a microarcsecond? See bellow to have an idea.
 1 degree = 1° = 1/360 of a circle
 1 arcminute = 1' = 1/60 of a degree
 1 arcsecond = 1" = 1/60 of an arcminute = 1/3600 of a degree
 1 milliarcsecond = 1 mas = 1/1000 arcsecond = 1/3,600,000 of a degree
 1 microarcsecond = 1/1000 of an milliarcsecond = 1/3,600,000,000 of a degree
Is it usefull?
In astronomy, we often use angular measurements to describe the apparent size of an object in space and the apparent distances between objects.
The star Epsilon Eridani is close enough to the Sun that its distance can be measured by the method of parallax, which gives the angle (p) 310.74 miliarcseconds = 0.31074 arc seconds. This can be converted to 3.218 parsecs (distance unit equivalent to 3.26 light years).
Microarcsecond is used to detect Earthlike planets orbiting in the habitable zone (HZ) of Sunlike stars.
AngleMeasuring Instruments
Protractor
It is probabily the most basic anglemeasuring instrument, a common object used in school math classes. This instrument is normally semicircular and is often used by students in the classroom.
Theodolite
A theodolite is a relatively complex type of anglemeasuring instrument that is used mainly by surveyors in civil engineering roles. It consists of a telescope that the user can look through to see a circular shape marked out in degrees, minutes and seconds (º ' "). At this level of detail the surveyor measurements can be very accurate. It is an optical instrument based on the telescope that is used for determining the horizontal and vertical angles between two points and for calculating distances.
Goniometer
Consists of a circular dial with degree measurements around the outside and tens of degrees in an inner circle. It has two arms, one that remains stationary and one that is movable.
Digital AngleMeasuring Devices
If we want to measure a simple angle, for instance in construction, we can use a digital anglemeasuring instrument to get a quick answer. These devices have two arms, which can be inserted into a corner and moved to fit the angle. A digital display then shows the measurement in degrees.
Units  Values  

Turns  0  1/24  1/12  1/10  1/8  1/6  1/5  1/4  1/3  2/5  1/2  3/4  1 
Radians  0  π/12  π/6  π/5  π/4  π/3  2π/5  π/2  2π/3  4π/5  π  3π/2  2π 
Degrees  0°  15°  30°  36°  45°  60°  72°  90°  120°  144°  180°  270°  360° 
Grads  0^{g}  16⅔^{g}  33⅓^{g}  40^{g}  50^{g}  66⅔^{g}  80^{g}  100^{g}  133⅓^{g}  160^{g}  200^{g}  300^{g}  400^{g} 