Convert Radians to Gradians (rad to gon)
1 radian (rad) = 63.66197724 gradians (gon). 1 gon = 0.01570796327 rad. Example: 15 rad = 15 × 63.66197724 = 954.9296586 gon.
Also searched as radians to gon, radians in gon, radians into gradians, rad to gon, rad in gradians, rad into gradian, radian to gradian, rad to gradians converter and how many gradians in a radian.
1 rad = 63.66197724 gon
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian to gradian converter to paste a column from Excel.
How to Convert Radian to Gradian
- 1 rad = 63.66197724 gon
- 1 gon = 0.01570796327 rad
- Example: convert 15 rad to gon: 15 rad = 15 × 63.66197724 gon = 954.9296586 gon
Formula
gon = rad × 63.66197723676
Derivation from SI units:
- The SI unit of plane angle: the angle subtended at the centre of a circle by an arc equal in length to the radius (1 rad = 1 m/m).
- 1 gon = π/200 rad; a right angle is 100 gon and a full turn 400 gon.
Both units are defined exactly, so the factor is exact. Radian definition: radian; Gradian definition: gradian.
Worked examples
- A reading of 2 rad converts to 127.3239545 gon.
2 rad × 63.66197724 = 127.3239545 gon - A value of 4 rad is 254.6479089 gon.
4 rad × 63.66197724 = 254.6479089 gon
Radian to Gradian conversion table
| Radians (rad) | Gradians (gon) |
|---|---|
| 0.5 rad | 31.83098862 gon |
| 1 rad | 63.66197724 gon |
| 1.5 rad | 95.49296586 gon |
| 2 rad | 127.3239545 gon |
| 3 rad | 190.9859317 gon |
| 3.14159 rad | 199.9998311 gon |
| 4 rad | 254.6479089 gon |
| 5 rad | 318.3098862 gon |
| 6 rad | 381.9718634 gon |
| 6.28318 rad | 399.9996621 gon |
Where it's used
Radians are used for trigonometry and calculus (derivatives of sin and cos assume radians), while gradians appear in land surveying in Europe. Both measure plane angle, so the conversion is a fixed factor.
Radian to other angle units
| Conversion | 1 rad equals |
|---|---|
| radian to gradian | 63.66197724 gon |
| radian to degree | 57.29577951 ° |
| radian to revolution | 0.1591549431 rev |
| radian to minute of arc | 3437.746771 ′ |
| radian to second of arc | 206264.8062 ″ |
Frequently asked questions
How many gradians are in 1 radian?
1 rad = 63.66197724 gon.
How do I convert radians to gradians?
Multiply the value in rad by 63.66197724. For example, 15 rad × 63.66197724 = 954.9296586 gon.
Is the rad to gon conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 4 (radian) and Table 8 (non-SI units accepted for use with the SI).
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology , Appendix B.8, "grad".
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Radians to Gradians (rad to gon). Retrieved October 25, 2026, from https://scientificconverters.com/angle/radians-to-gradians/
IEEE
Scientific Converters, "Convert Radians to Gradians (rad to gon)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/radians-to-gradians/