Convert degree to radian

What is a degree?

Degrees are depicted by the symbol ° and utilized for the determination of angles. The word itself comes from Latin and designates the part of the scale. When we think about 360°, we imagine a full rotation and 90° are perceived as the right angle.

There is no one opinion on the question of why a degree was chosen as a unit and why it has such values. Most of the explanations refer to ancient times and systems that were utilized by our predecessors. Thus, the Persians used a calendar with 360 days and the similar system was also common in Babylon. Another interesting fact is that 1 deg is almost equal to 1 cm in the circle with a 57 cm radius.

Nowadays degrees are not a standard unit. However, they are widely used and have an easy relation to radians. Thus, one deg corresponds to π/180 radians.

What is a radians?

Humans were fascinated by circles since ancient times. Looking at the sun and the moon our predecessors wanted to create something similar. Thus, plates, baskets and wheels appeared.

A full rotation was given a value of 360 degrees. Later it was noted that the circumference and diameter of the circle always have the same ratio. This fact led to the introduction of π value, the calculation of the circumference as 2πr and the appearance of a radian.

Radians are modern standard units without dimensions. One rad corresponds to approximately 57 deg. The definition says that it is the angle on a circle, on which the arc lies the radius of that circle.

When you encounter an angle of 2 rad, then you should imagine one of 114 deg. If there is π rad, it means 180 deg. At last, a full circle corresponds to 2π radians.