How to convert radians to degrees

To measure an angle, there are two different measuring systems. The two units used to measure an angle are radians and degrees. The unit radians is used mostly in the concept of trigonometry. The measure of angles can be converted from radians to degrees using a formula. To understand this formula and conversion of radians to degrees, we will understand the meaning of each unit of angle. We will also see the conversion table for radians to degrees in this article.

Radians to Degrees Conversion

There are two different units used to measure an angle: radians and degrees. Hence, it is important for us to be proficient in the conversion of units of angle, that is radians to degrees and degrees to radians. When we take the radius of a circle and revolve it, we start constructing an angle that can be measured in radians or degrees. Let us see what each unit of angle means and how to measure the angle.

Radians

When we rotate the radius completely around the circle, it completes one rotation. The angle subtended at the center of the circle by the radius after one complete rotation is 2π radians. The angle in radians subtended by the radius at the center of the circle is the ratio of the length of the arc to the length of the radius. When the length of the arc becomes equal to the length of the radius, the angle subtended at the center becomes 1 radian. We denote the unit radian as rad. Radians is the SI unit of measuring angles.

Degrees

Angles are measured in degrees. One revolution is divided into 360 equal parts and each part is called a degree. The angle subtended at the center of the circle after one complete rotation of the radius is 360°. The symbol for degrees is denoted by '°'. Degrees is not an SI unit to measure angles but it is an accepted unit to measure. Hence, while solving problems, it is preferred to convert the unit of angle from radians to degrees to understand it better. The instrument used to measure an angle in degrees is a protractor.
Comparing the measures of the angle for a complete rotation, we observe,

• 360 Degrees = 2π Radians

• 180 Degrees = π Radians

Radians to Degrees Formula

The radians to degrees formula is used to convert radians to degrees. To convert radians to degrees we need to multiply the radians by 180°/π radians. When we measure angles we use two types of units: degrees and radians, 1 degree is written as 1°. And 1 radian is written as 1 (or) 1c i.e. if there is no unit after the measure of an angle, it means that it is in radians. One rotation in a circle is divided into 360 equal parts and each part is called a degree. One complete counterclockwise rotation in radians is 2π and in degrees, it is 360°. Thus, degree measure and radian measure are related. The formula to convert an angle in radians to degrees is:
Angle in Radians × 180°/π = Angle in Degrees

One degree is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

One radian is equal 57.295779513 degrees:

1 rad = 180°/π = 57.295779513°

The angle α in degrees is equal to the angle α in radians times 180 degrees divided by pi constant:

α_(degrees) = α_(radians) × 180° / π

or

degrees = radians × 180° / π

Example

Convert 0.5236 rad angle to degrees:

α_(degrees) = α_(radians) × 180° / π = 0.5236 rad × 180° / 3.1459 = 30°

How to convert degrees to radians »