Degrees to Radians Converter
Type a value in degrees to see it in radians. It works both ways: type in the radians box to convert back.
Formula
To convert degrees to radians, divide by 57.29577951 (the same as multiplying by 0.01745329252).
1 ° = 0.0174532925199 rad and 1 rad = 57.2957795131 °.
Degrees to radians table
| Degrees | Radians |
|---|---|
| 0 ° | 0 rad |
| 15 ° | 0.2617994 rad |
| 30 ° | 0.5235988 rad |
| 45 ° | 0.7853982 rad |
| 60 ° | 1.047198 rad |
| 90 ° | 1.570796 rad |
| 120 ° | 2.094395 rad |
| 135 ° | 2.356194 rad |
| 180 ° | 3.141593 rad |
| 270 ° | 4.712389 rad |
| 360 ° | 6.283185 rad |
Worked examples
15 ° in radians
15 °
0.2617994 rad
15 × 0.01745329252 = 0.2617993878
90 ° in radians
90 °
1.570796 rad
90 × 0.01745329252 = 1.570796327
270 ° in radians
270 °
4.712389 rad
270 × 0.01745329252 = 4.71238898
About Degrees to Radians Converter
This converter turns degrees into radians as you type, and works the other way too: type in the radians box to convert back. To convert degrees to radians, divide by 57.29577951 (the same as multiplying by 0.01745329252). For example, 15 ° is 0.2617994 rad, and 90 ° is 1.570796 rad.
Degrees are the everyday unit for angles, but maths, physics and programming languages use radians, where a full turn is 2π. Both units have exact definitions, so the converter gives an exact result, rounded only for display. Use the table below for common values, or set the decimal places to round the answer for a form or a label.
How to use Degrees to Radians Converter
- Type the amount in degrees in the first box.
- Read the answer in radians in the second box and in the result line below.
- To convert the other way, type in the radians box instead, or use the swap button to open the radians to degrees page.
- Choose a number of decimal places if you need a rounded figure, then copy the result line.
Common uses
- Programming with trigonometry functions
- Maths and physics homework
- Engineering and CAD drawings
- Checking angles from a protractor or a design tool
Frequently asked questions
How many radians are in one degree?
There are 0.01745329252 radians in one degree. This figure is exact, because both units have fixed definitions.
How do I convert degrees to radians?
To convert degrees to radians, divide by 57.29577951 (the same as multiplying by 0.01745329252). For example, 270 ° is 4.712389 rad.
How do I convert radians to degrees?
Going the other way, multiply by 57.29577951. The radians to degrees converter does this for you.
What is 135 ° in radians?
135 ° is 2.356194 rad.
Why do programming languages use radians?
Radians make the maths of curves and circles simpler, because an angle in radians equals the arc length on a circle of radius 1. Functions like sin and cos are defined in radians, so most languages expect them.