Degrees to Radians Converter
One Degree equals 0.01745329252 Radians (1 deg = 0.01745329252 rad). Multiply a Degree value by 0.01745329252 to get the equivalent in Radians. Enter a value above to calculate the result. You can also use the formula and reference table below.
Formula
rad = deg × 0.01745329252
Multiply the Degree value by 0.01745329252 to get the equivalent value in Radians.
Example Conversions
1 Degree (deg)
0.01745329252 Radian (rad)
5 Degree (deg)
0.0872664626 Radian (rad)
10 Degree (deg)
0.1745329252 Radian (rad)
25 Degree (deg)
0.436332313 Radian (rad)
100 Degree (deg)
1.745329252 Radian (rad)
Conversion Table
| Degree (deg) | Radian (rad) |
|---|---|
| 0.1 | 0.001745329252 |
| 0.5 | 0.00872664626 |
| 1 | 0.01745329252 |
| 2 | 0.03490658504 |
| 5 | 0.0872664626 |
| 10 | 0.1745329252 |
| 25 | 0.436332313 |
| 50 | 0.872664626 |
| 100 | 1.745329252 |
| 250 | 4.36332313 |
| 500 | 8.72664626 |
| 1000 | 17.45329252 |
How to Convert Manually
Use these steps to convert Degree values to Radian without the calculator.
- Write down the value in Degree (deg) that you want to convert.
- Multiply that value by 0.01745329252.
- For example, 10 Degrees × 0.01745329252 = 0.1745329252 Radians.
- Label the result as Radian (rad).
Relative Size Comparison
This chart shows the visual difference in size between exactly one Degree and one Radian.
About Degree and Radian
The degree is 1/360 of a full turn, a division inherited from Babylonian astronomy. Navigation, geometry, and everyday angle measurement default to degrees. The radian is the SI unit of angle: the angle whose arc length equals its radius, with 2π radians in a full turn. Calculus, physics, and programming math libraries work in radians. One Degree equals 0.01745329252 Radians (1 deg = 0.01745329252 rad). Degree is used in navigation headings and in geometry and CAD drawings. Radian is used in physics and engineering formulas.
Precision and Rounding:Angle conversions are exact ratios of a full turn, but radian values involve π and never terminate in decimal form. Navigation and construction round to whole degrees or minutes; surveying, astronomy, and robotics carry six or more significant figures.
Conversion factors per NIST Special Publication 811 and the BIPM SI Brochure (9th edition) (reference).
Worked Example
15Degrees equals0.2617993878Radians.
15 deg × 0.01745329252 = 0.2617993878 rad
FAQ
How do I convert Degree to Radian?
Multiply the Degree value by 0.01745329252 to get the equivalent value in Radians.
What is the formula for Degree to Radian?
The formula is rad = deg × 0.01745329252.
How many Radians are in 1 Degree?
1 Degree equals 0.01745329252 Radians.
Can I convert Radian back to Degree?
Yes. 1 Radian equals 57.29577951 Degrees, and the related converter can reverse the calculation.
What are common names for Degree and Radian?
Degree is shown as deg and may also be searched as degree, degrees, °. Radian is shown as rad and may also be searched as radian, radians.
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