Convert Radians to Gradians
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Science
About Angle Conversions
Angle measurements are fundamental in mathematics, engineering, navigation, and astronomy. The degree, divided into 60 arcminutes and 3,600 arcseconds, has been the standard angular unit since ancient Babylonian mathematics. The radian — the SI unit of angle — relates arc length directly to radius and simplifies calculus-based calculations: a full circle equals exactly 2π radians. Gradians (also called gons) divide a right angle into exactly 100 units, making them popular in surveying and civil engineering across continental Europe. Revolutions (full turns) are common in mechanical engineering for expressing rotation speed. Our converter uses exact mathematical relationships: 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 Gradians?
To convert Radians to Gradians, use the conversion where 1 Radian (rad) = 63.662 Gradians (gon). For example, 1 Radian = 63.662 Gradians.
What are common Radian to Gradian conversions?
Here are common conversions: 1 Radians = 63.662 Gradians, 5 Radians = 318.31 Gradians, 10 Radians = 636.62 Gradians, 25 Radians = 1591.55 Gradians, 50 Radians = 3183.1 Gradians, 100 Radians = 6366.2 Gradians.
When would I need to convert Radians to Gradians?
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.