Convert Degrees to Radians
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Science
About Angle Conversions
Angles run through math, engineering, navigation, and astronomy. The degree, split into 60 arcminutes and 3,600 arcseconds, has been the standard since Babylonian mathematics. The radian, the SI unit, ties arc length straight to radius and is what makes calculus on circles clean: a full turn is exactly 2π radians. Gradians, or gons, cut a right angle into exactly 100 parts, which is why surveyors and civil engineers across continental Europe favor them. Revolutions, full turns, show up in mechanical work for rotation speed. The identities below are exact: 1 revolution = 360° = 2π rad = 400 gon.
Quick Conversions
| Unit Name | Symbol | Per 1 Degree |
|---|---|---|
| Arcminute | ′ | 60 |
| Arcsecond | ″ | 3600 |
| Degree | ° | 1 |
| Gradian | gon | 1.11111 |
| Radian | rad | 0.0174533 |
| Revolution | rev | 0.00277778 |
Frequently Asked Questions
How do I convert Degrees to Radians?
To convert Degrees to Radians, use the conversion where 1 Degree (°) = 0.0174533 Radians (rad). For example, 1 Degree = 0.0174533 Radians.
What are common Degree to Radian conversions?
Here are common conversions: 1 Degrees = 0.0174533 Radians, 5 Degrees = 0.0872665 Radians, 10 Degrees = 0.174533 Radians, 25 Degrees = 0.436332 Radians, 50 Degrees = 0.872665 Radians, 100 Degrees = 1.74533 Radians.
When would I need to convert Degrees to Radians?
Converting between these units is common in international trade, scientific research, and everyday situations where different measurement systems are used.
How precise are the conversions?
All conversions use exact factors verified against NIST and ISO standards with up to 10 significant figures of precision. Results are calculated using IEEE 754 double-precision arithmetic, which provides approximately 15-17 significant digits. For temperature and other non-linear conversions, exact formulas are used rather than approximations.