How to Convert Degrees to Radians

Step-by-step solution

1. Multiply the degrees by pi/180.

   $$135^\circ \times \frac{\pi}{180^\circ}$$

   Why: A full turn is 360 degrees or 2pi radians, so the factor between them is pi/180.

2. Multiply the numbers.

   $$\frac{135\pi}{180}$$

   Why: The degree symbols cancel.

3. Simplify the fraction by 45.

   $$\frac{135\pi}{180} = \frac{3\pi}{4}$$

   Why: 135 divided by 45 is 3, and 180 divided by 45 is 4.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $90^\circ$

   Show answer

   $\frac{\pi}{2}$

2. 2

   $180^\circ$

   Show answer

   $\pi$

3. 3

   $60^\circ$

   Show answer

   $\frac{\pi}{3}$

4. 4

   $45^\circ$

   Show answer

   $\frac{\pi}{4}$

5. 5

   $270^\circ$

   Show answer

   $\frac{3\pi}{2}$