The degree
The degree (°) divides a full rotation into 360 equal parts, a convention traced to Babylonian sexagesimal astronomy. It is the everyday unit for angles in navigation, geography (latitude/longitude), construction, and general use.
Degrees to Radians Converter
1 ° = 0.0174533 rad (degree → radian)
1 ° = 0.0174533 rad
1 degree equals 0.0174533 radians. To convert degrees to radians, multiply the degree value by 0.0174533. For quick reference: 1 ° = 0.0174533 rad, 5 ° = 0.0872665 rad, 10 ° = 0.174533 rad, 100 ° = 1.74533 rad.
Formula
Radians = Degrees × 0.0174533Quick
How to convert degrees to radians
Take your value
Start with your value in degrees.
Multiply by 0.0174533
Multiply the degree value by 0.0174533. This is the exact conversion factor from degrees to radians.
Read the result
The product is your value in radians. For example, 5 ° × 0.0174533 = 0.0872665 rad.
Conversion formula
The exact factor from degrees to radians is 0.0174533.
Radians = Degrees × 0.0174533
Degrees to Radians conversion table
Fifty common reference values, hand-picked for skim utility. Use the calculator above for any value not listed.
| Degrees (°) | Radians (rad) |
|---|---|
| 0.1 ° | 0.0017453 rad |
| 0.25 ° | 0.0043633 rad |
| 0.5 ° | 0.0087266 rad |
| 1 ° | 0.017453 rad |
| 2 ° | 0.034907 rad |
| 3 ° | 0.05236 rad |
| 4 ° | 0.069813 rad |
| 5 ° | 0.087266 rad |
| 6 ° | 0.10472 rad |
| 7 ° | 0.12217 rad |
| 8 ° | 0.13963 rad |
| 9 ° | 0.15708 rad |
| 10 ° | 0.17453 rad |
| 11 ° | 0.19199 rad |
| 12 ° | 0.20944 rad |
| 13 ° | 0.22689 rad |
| 14 ° | 0.24435 rad |
| 15 ° | 0.2618 rad |
| 16 ° | 0.27925 rad |
| 18 ° | 0.31416 rad |
| 20 ° | 0.34907 rad |
| 22 ° | 0.38397 rad |
| 24 ° | 0.41888 rad |
| 25 ° | 0.43633 rad |
| 28 ° | 0.48869 rad |
| 30 ° | 0.5236 rad |
| 32 ° | 0.55851 rad |
| 36 ° | 0.62832 rad |
| 40 ° | 0.69813 rad |
| 45 ° | 0.7854 rad |
| 48 ° | 0.83776 rad |
| 50 ° | 0.87266 rad |
| 60 ° | 1.0472 rad |
| 70 ° | 1.2217 rad |
| 75 ° | 1.309 rad |
| 80 ° | 1.3963 rad |
| 90 ° | 1.5708 rad |
| 100 ° | 1.7453 rad |
| 125 ° | 2.1817 rad |
| 150 ° | 2.618 rad |
| 200 ° | 3.4907 rad |
| 250 ° | 4.3633 rad |
| 300 ° | 5.236 rad |
| 400 ° | 6.9813 rad |
| 500 ° | 8.7266 rad |
| 600 ° | 10.472 rad |
| 750 ° | 13.09 rad |
| 800 ° | 13.963 rad |
| 900 ° | 15.708 rad |
| 1000 ° | 17.453 rad |
Real-world reference
A right angle is 90°. A straight line is 180°. In radians, that gives you: 1 ° = 0.0174533 rad, 10 ° = 0.174533 rad, 100 ° = 1.74533 rad.
Frequently asked questions
- How many radians are in 1 degree?
- 1 degree equals 0.0174533 radians.
- How do I convert degrees to radians?
- Multiply the degree value by 0.0174533. So x ° × 0.0174533 = the equivalent in rad.
- What is 5 degrees in radians?
- 5 degrees equals 0.0872665 radians.
- What is 10 degrees in radians?
- 10 degrees equals 0.174533 radians.
- What is 100 degrees in radians?
- 100 degrees equals 1.74533 radians.
- How do I convert back from radians to degrees?
- Multiply the radian value by 57.2958. For example, 1 rad = 57.2958 °.
- Is the degree bigger than the radian?
- No. 1 degree is smaller than 1 radian. It takes 57.2958 degrees to equal 1 radian.
- Are these conversion factors exact?
- The factor is derived directly from the SI definitions of degree and radian; the displayed value is rounded for readability, and the browser computes using IEEE 754 double-precision arithmetic.
About the degree and the radian
The radian
The radian (rad) is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full turn equals exactly 2π radians (≈6.2832 rad). It is the standard unit in mathematics, physics, and engineering calculations.