Degree to Radian Converter
Convert Degree to Radian — free, instant, accurate. Part of Angle converters.
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Degree to Radian: values and formula
1 Degree = 0.0174532863 Radian, and 1 Radian = 57.2958 Degree. To convert a angle value from Degree to Radian, multiply it by 0.0174532863. For example, 10 Degree equals 0.1745328628 Radian, and 250 Degree equals 4.3633215698 Radian.
| Degree | Radian |
|---|---|
| 1 Degree | 0.0174532863 Radian |
| 2 Degree | 0.0349065726 Radian |
| 5 Degree | 0.0872664314 Radian |
| 10 Degree | 0.1745328628 Radian |
| 25 Degree | 0.436332157 Radian |
| 50 Degree | 0.872664314 Radian |
| 100 Degree | 1.7453286279 Radian |
| 500 Degree | 8.7266431396 Radian |
| 1000 Degree | 17.453286279 Radian |
When to use the Degree to Radian converter
- Mathematics and trigonometry — switching between degrees and radians.
- Surveying — using gradians for slope and bearing.
- Astronomy — measuring small angles in arcminutes and arcseconds.
- Navigation — reading bearings in degrees.
A short history of angle units
Angles were originally divided into 360 degrees by Babylonian astronomers using their base-60 number system. The radian, defined as the angle subtended by an arc equal to the radius, emerged in mathematical analysis in the 18th century. The gradian (or gon) divides a quarter circle into 100 parts and survives in surveying.
Common mistakes when converting angle
Calculator mode
Setting the calculator to the wrong mode (DEG vs RAD) is the most common source of trig errors.
Arcminute vs minute
1 arcminute is 1/60 of a degree (an angle), not a unit of time.
Gradian misuse
90° equals 100 gradians, not 90 or 360. Surveyors use it because right angles are round numbers.
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