Convert Degree to Radian
Unit definitions
Degree
The degree is a unit of angle commonly used in daily life. One full circle consists of $360$ degrees.
Radian
The radian is the unit of angle in the SI. A full circle is $2\pi$ radians, where $\pi$ is approximately $3.141\,592\,653\,589\,793$.
How to convert Degree to Radian
$$\text{Angle}_{\text{rad}} = \frac{\text{Angle}_{\text{°}}}{180} \cdot 3.141592653589793$$
Examples
Example 1
Convert $45.0\ \text{°}$ to $\text{rad}$.
$$\text{Angle}_{\text{rad}} = \frac{45.0}{180} \cdot 3.141592653589793$$
$$\text{Angle}_{\text{rad}} = 0.785398$$
$$\therefore \ 45.0\ \text{°} = 0.785398 \ \text{rad}$$
Example 2
Convert $60.0\ \text{°}$ to $\text{rad}$.
$$\text{Angle}_{\text{rad}} = \frac{60.0}{180} \cdot 3.141592653589793$$
$$\text{Angle}_{\text{rad}} = 1.047198$$
$$\therefore \ 60.0\ \text{°} = 1.047198 \ \text{rad}$$
Example 3
Convert $115.0\ \text{°}$ to $\text{rad}$.
$$\text{Angle}_{\text{rad}} = \frac{115.0}{180} \cdot 3.141592653589793$$
$$\text{Angle}_{\text{rad}} = 2.007129$$
$$\therefore \ 115.0\ \text{°} = 2.007129 \ \text{rad}$$
Example 4
Convert $130.0\ \text{°}$ to $\text{rad}$.
$$\text{Angle}_{\text{rad}} = \frac{130.0}{180} \cdot 3.141592653589793$$
$$\text{Angle}_{\text{rad}} = 2.268928$$
$$\therefore \ 130.0\ \text{°} = 2.268928 \ \text{rad}$$
Example 5
Convert $195.0\ \text{°}$ to $\text{rad}$.
$$\text{Angle}_{\text{rad}} = \frac{195.0}{180} \cdot 3.141592653589793$$
$$\text{Angle}_{\text{rad}} = 3.403392$$
$$\therefore \ 195.0\ \text{°} = 3.403392 \ \text{rad}$$
Degree to Radian conversion table
Convert Degree to other Angle units
| Degree [°] | Other unit |
|---|---|
| 1 | 6E+1 Arcminute (Minute Angle) [′] |
| 1 | 3.6E+3 Arcsecond (Second Angle) [′′] |
| 1 | 0.002778 Revolution [rev] |
| 1 | 1.745329 Centiradian [centiradian] |
| 1 | 1.111111 Grade [grad] |