Degrees to Radians (° to rad) Converter
1 degree (°) = 0.0174533 radians (rad). To convert degrees to radians, multiply by 0.0174533: 90 ° × 0.0174533 = 1.5708 rad.
Quick facts
- 1 ° = 0.0174533 rad
- 1 rad = 57.2958 °
- Formula: rad = ° × 0.0174533
- Quick estimate: multiply by about 0.017
How to convert degrees to radians
- Take the value in degrees.
- Multiply it by 0.0174533 (the number of radians in one degree).
- Round the result to the precision you need.
Worked example (a right angle): 90 ° × 0.0174533 = 1.5708 rad.
To convert radians back to degrees, multiply by 57.2958, or divide by 0.0174533.
Source: BIPM SI Brochure, 9th edition (the radian).
Degrees to Radians conversion table
| Degrees [°] | Radians [rad] |
|---|---|
| 0.01 ° | 0.0001745329 rad |
| 0.1 ° | 0.0017453293 rad |
| 1 ° | 0.0174532925 rad |
| 2 ° | 0.034906585 rad |
| 3 ° | 0.0523598776 rad |
| 5 ° | 0.0872664626 rad |
| 10 ° | 0.1745329252 rad |
| 20 ° | 0.3490658504 rad |
| 50 ° | 0.872664626 rad |
| 100 ° | 1.745329252 rad |
| 1000 ° | 17.4532925199 rad |
° to rad chart from 1 to 100
- 1 ° 0.0174533 rad
- 2 ° 0.0349066 rad
- 3 ° 0.0523599 rad
- 4 ° 0.0698132 rad
- 5 ° 0.0872665 rad
- 6 ° 0.10472 rad
- 7 ° 0.122173 rad
- 8 ° 0.139626 rad
- 9 ° 0.15708 rad
- 10 ° 0.174533 rad
- 11 ° 0.191986 rad
- 12 ° 0.20944 rad
- 13 ° 0.226893 rad
- 14 ° 0.244346 rad
- 15 ° 0.261799 rad
- 16 ° 0.279253 rad
- 17 ° 0.296706 rad
- 18 ° 0.314159 rad
- 19 ° 0.331613 rad
- 20 ° 0.349066 rad
- 25 ° 0.436332 rad
- 30 ° 0.523599 rad
- 35 ° 0.610865 rad
- 40 ° 0.698132 rad
- 45 ° 0.785398 rad
- 50 ° 0.872665 rad
- 55 ° 0.959931 rad
- 60 ° 1.0472 rad
- 65 ° 1.13446 rad
- 70 ° 1.22173 rad
- 75 ° 1.309 rad
- 80 ° 1.39626 rad
- 85 ° 1.48353 rad
- 90 ° 1.5708 rad
- 95 ° 1.65806 rad
- 100 ° 1.74533 rad
Radians to Degrees conversion table
| Radians [rad] | Degrees [°] |
|---|---|
| 0.01 rad | 0.5729577951 ° |
| 0.1 rad | 5.7295779513 ° |
| 1 rad | 57.2957795131 ° |
| 2 rad | 114.5915590262 ° |
| 3 rad | 171.8873385392 ° |
| 5 rad | 286.4788975654 ° |
| 10 rad | 572.9577951308 ° |
| 20 rad | 1145.9155902616 ° |
| 50 rad | 2864.7889756541 ° |
| 100 rad | 5729.5779513082 ° |
| 1000 rad | 57295.7795130823 ° |
Degrees vs Radians
| Degree | Radian | |
|---|---|---|
| Symbol | ° | rad |
| Equals | 1 ° = 0.0174533 rad | 1 rad = 57.2958 ° |
What is a degree?
One 360th of a full rotation. The everyday unit for angles in geometry, navigation, and construction.
What is a radian?
The SI unit of angle, where one full rotation equals 2π radians. Used throughout calculus, physics, and engineering.
Frequently asked questions
How many radians are in a degree?
There are 0.0174533 radians in 1 degree (1 ° = 0.0174532925 rad).
How many degrees are in a radian?
There are 57.2958 degrees in 1 radian (1 rad = 57.2957795131 °).
How do I convert degrees to radians?
Multiply the number of degrees by 0.0174533. For example, 10 ° × 0.0174533 = 0.174533 rad. To convert back, multiply by 57.2958.
What is 10 ° in radians?
10 ° = 0.174533 rad.
What is 100 ° in radians?
100 ° = 1.74533 rad.
Is the conversion exact?
Yes. The factor comes from the official definitions of both units (BIPM SI Brochure, 9th edition (the radian)). Results are shown to up to 10 decimal places; round them to suit your purpose.
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