Convert Radians to Degrees
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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 Radian |
|---|---|---|
| Arcminute | ′ | 3437.75 |
| Arcsecond | ″ | 206265 |
| Degree | ° | 57.2958 |
| Gradian | gon | 63.662 |
| Radian | rad | 1 |
| Revolution | rev | 0.159155 |
Frequently Asked Questions
How do I convert Radians to Degrees?
To convert Radians to Degrees, use the conversion where 1 Radian (rad) = 57.2958 Degrees (°). For example, 1 Radian = 57.2958 Degrees.
What are common Radian to Degree conversions?
Here are common conversions: 1 Radians = 57.2958 Degrees, 5 Radians = 286.479 Degrees, 10 Radians = 572.958 Degrees, 25 Radians = 1432.39 Degrees, 50 Radians = 2864.79 Degrees, 100 Radians = 5729.58 Degrees.
When would I need to convert Radians to Degrees?
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.
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How this result is maintained
Calcflux publishes the formula, assumptions, limits, and primary references behind its tools. Automated tests guard the implemented calculation paths and known-answer cases.
Conversions keep full numeric precision through the calculation and round only the displayed result.
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- Verification
- Formula tests and boundary checks