This post is to clarify the unit of angle of rotation, many times is it observed that some people get confused when it comes to angle measurement, particularly small angle. Most common unit being Degree and gradian. One full circle consists of angle 360 degree or 400 gradian. Our focus now is on angle unit in degree in this writeup. We know a circle consists of 4 parts of 90 degree angle or two parts of 180 degree angle.

Total circle is therefore 360 degree angle, least value as a whole number will be 1 degree of angle and fraction will be 0.1, 0.2 0.3 ….. and so on angle in degree. But if the decimal value increases it becomes difficult to write and understand the value of angle in degree. Hence the fraction can be mentioned in minute and second, in a same way as we read the clock.

As the clock is read in fraction that is one hour consists of 60 minutes and 1 minute consists of 60 seconds, in a same was 1 degree of angle is equal to 60 minutes and 1 minute is equal to 60 second of angle. If we table out the value it will look something like shown below.

Angle of rotation
1 degree =	60 minutes
1 minute =	60 seconds
1 degree =	3600 seconds

As we can see from the table above 1 degree of angle is divided in 3600 parts and each part is called as 1 second of angle or 1 arc second of angle. Now instead of writing 0.00027778 degree we can write as 1 second (ignoring the value after 4 decimal).

Many times, we are required to measure small angle value or measure the angle with high precision. Like in construction industry where imagine a building being constructed consisting of 10 floors, where the height of the building may be more than 100 feet. In such case it is very important to measure the angle of building with high precision as the building may get tilted. Another example can be a structure holding the rocket for launch, it calls for high precision in such constructions.

In order to measure such precision value measuring device will have unit of angle in degree, minute and second. Example of such device is Total Station, Theodolite. Laboratory instruments where it is required to measure angle, like collimator also have measurement of angle in arc second.