# What are the proper units for measuring angles?

Apr 30, 2017

1 - The most popular unit is degree, minutes and seconds. In this there are $90$ degrees in a right angle or $360$ degrees in a complete circle and for finer calculations, each degree is divided in $60$ parts each called a minute , and further each minute is divided in $60$ parts with each part being called a second .
2 - We also use the unit radian. It is a bit complicated as in one complete circle there are $2 \pi$ radians ($\pi = 3.14159265359 \ldots \ldots .$) and $\frac{\pi}{2}$ radians in each right angle. This is mostly use in mathematical calculations.
3 - The third type of unit for measuring angles is grad (from gradient). This was an attempt to bring decimal system for angles, as each right angle was divided into $100$ grads (and $400$ grads for a circle). Further, each grad is divided in $100$ parts each called a minute , and further each minute is divided in $100$ parts with each part being called a second .