# Degree and Radian Measure Formula

In mathematics, the radian is the standard unit of angular measure. An angle’s measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. The relationship or the connection between the arc length and radius of a circle defines the radian of a circle. Degree and radian formula used to convert, degree to radian or radian to degree.

$\LARGE Radian=\frac{Arc\;Length}{Radius\;Length}$

$\LARGE Radian=\frac{Degree\times \pi}{180}$

Here are few Degree Measures and their corresponding Radian Measures –Â

30Â° = Ï€/6

45Â° = Ï€/4

60Â° = Ï€/3

90Â° = Ï€/2

120Â° = 2Ï€/3

135Â° = 3Ï€/4

150Â° = 5Ï€/6

180Â° = Ï€

210Â° = 7Ï€/6

225Â° = 5Ï€/5

240Â° = 4Ï€/3

270Â° = 3Ï€/2

300Â° = 5Ï€/3

315Â° = 7Ï€/4

330Â° = 11Ï€/6

360Â° = 2Ï€

### Solved Example

Question:

Solution:

Given,

DegreeÂ = 220Â°

We know that,

$$\begin{array}{l}\frac{degree \times \pi}{180}\end{array}$$

$$\begin{array}{l}\frac{220 \times \pi}{180}\end{array}$$
$$\begin{array}{l}\frac{11 \times \pi}{9}\end{array}$$
$$\begin{array}{l}0.837\end{array}$$