Degrees to Radians Calculator

How to Convert Degrees to Radians

To convert degrees to radians, you need to use the conversion formula. Since π radians equals 180°, you can use the following formula to convert degrees to radians:

radians = degrees × π/180

In other words, the radian angle equals the degree angle multiplied by π, then divided by 180.

To use this formula, first substitute the degree value of the angle into the formula. Then, move the degree value to the numerator of the fraction, and finally simplify the fraction and compute the result.

For example, let us use this formula to convert 5 degrees to radians.

radians = 5° × π/180
radians = 5° × π/180
radians = 1 × π/36
radians = π/36

What is a Radian?

A radian is a unit of angular measurement equal to the length of the arc divided by the radius of the circle or arc. 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, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.
Radians are commonly expressed by 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. Therefore, a radian can also be expressed as the formula for arc length divided by radius.
The radian is also considered a "dimensionless" unit. That is, when multiplying or dividing by radians, the final unit does not include radians.
For example, when calculating the arc length of a given angle, we use the above formula and rearrange it as s = θr. If θ is in radians and r is in meters, then s has the unit of meters, not radian-meters. However, if θ is in degrees, then s has the unit of degree-meters.

Common Radian-Degree Conversion Table

Radians	Degrees	π Representation
0	0°	0
π/6	30°	≈0.5236
π/4	45°	≈0.7854
π/3	60°	≈1.0472
π/2	90°	≈1.5708
π	180°	≈3.1416
3π/2	270°	≈4.7124
2π	360°	≈6.2832