What is an angle?

Angle is a unit of measurement used to describe the included angle between two line segments. Our usual degree system is to divide a complete circle into 360 parts, each of which is 1. For example, the two sides of a right angle make 90 degrees with the horizontal and vertical directions respectively. When the angle is 45, they show equal inclination.

What is the radian?

Radian is a unit of measurement used to describe the proportional relationship between arc length and radius on a circle. Because the ratio of arc length to radius is a dimensionless value, radian is also a dimensionless unit. Under the radian system, the number of radians corresponding to a complete circle is 2π, that is, the circumference of the circle is equal to the diameter. So the angle corresponding to 1 radian is 180/π.

Conversion of angle and radian

Given 1 = π/ 180 rad, we can convert angles and radians through this proportional relationship. For example, how many radians is 5? We only need to multiply 5 by π/ 180 to get its corresponding radian value. The calculated result is 0.087266 radian.

Why do you want to convert angles and radians?

For most common mathematical and physical problems, angle system and arc system can be well described. But sometimes they are used in different situations. In mathematical analysis and vector operation, arc system is more convenient, because in these fields, concepts such as circumferential arc length, curve arc length and plane vector are often involved. Angle system is more practical in daily angle measurement and drawing.