Radians to Degrees Calculator

How to Convert Radians to Degrees

To convert radians to degrees, a conversion formula is required. Since π radians equals 180°, the following conversion formula is widely accepted in mathematics due to its accuracy and convenience.

 Angle = Radians × (180 / π) 

Here, π ≈ 3.141592653589793

In other words, degrees equal radians multiplied by 180 divided by π.
To use this formula, first substitute the angle (in radians) into the formula. Then, move the radians value to the numerator, and finally simplify the fraction and compute the result.

For example, let's use the primary formula to convert 5 radians to degrees.

Degrees = 5 radians × 180 / π
Degrees = 5 × 180 / π
Degrees = 900 / π

What is a Radian?

A radian is a unit of angular measurement, defined as the angle subtended at the center of a circle by an arc whose length equals the radius of the circle. One radian equals 180/π degrees, approximately 57.29578°. The radian measure of a full circle is approximately 6.28318.
The radian is the SI derived unit for angular measurement. Radians can be abbreviated as "rad", and sometimes as "c", "r", or "R". For example, one radian can be written as 1 rad, 1 c, 1 r, or 1 R.
Radians are commonly expressed using their definition. The formula for an angle in radians is θ = s/r, where the angle θ (in radians) equals the arc length s divided by the radius r. Thus, a radian can also be represented as the formula: arc length divided by radius.
The radian is also considered a "dimensionless" unit. This means that when multiplying or dividing by radians, the final unit does not include "radians".
For example, when calculating the arc length for a given angle, we rearrange the above formula to s = θr. If θ is measured in radians and r is measured in meters, then s is measured in meters—not "radian-meters". However, if θ is measured in degrees, then s is measured in "degree-meters".

Common Radian-Degree Conversion Table