Convert Degrees to Gradians (° to gon)
1 degree (°) = 1.111111111 gradians (gon). 1 gon = 0.9 °. Example: 15 ° = 15 × 1.111111111 = 16.66666667 gon.
Also searched as degrees to gon, degrees in gon, degrees into gradians, ° to gon, ° in gradians, ° into gradian, degree to gradian, ° to gradians converter and how many gradians in a degree.
1 ° = 1.111111111 gon
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk degree to gradian converter to paste a column from Excel.
How to Convert Degree to Gradian
- 1 ° = 1.111111111 gon
- 1 gon = 0.9 °
- Example: convert 15 ° to gon: 15 ° = 15 × 1.111111111 gon = 16.66666667 gon
Formula
gon = ° × 1.111111111111
Derivation from SI units:
- 1° = π/180 rad exactly; a full turn is 360°.
- 1 gon = π/200 rad; a right angle is 100 gon and a full turn 400 gon.
- 1 ° = 0.01745329251994 rad ÷ 0.01570796326795 rad per gon = 1.111111111111 gon
Both units are defined exactly, so the factor is exact. Degree definition: degree; Gradian definition: gradian.
Worked examples
- A reading of 45 ° converts to 50 gon.
45 ° × 1.111111111 = 50 gon - A value of 120 ° is 133.3333333 gon.
120 ° × 1.111111111 = 133.3333333 gon
Degree to Gradian conversion table
| Degrees (°) | Gradians (gon) |
|---|---|
| 1 ° | 1.111111111 gon |
| 15 ° | 16.66666667 gon |
| 30 ° | 33.33333333 gon |
| 45 ° | 50 gon |
| 60 ° | 66.66666667 gon |
| 90 ° | 100 gon |
| 120 ° | 133.3333333 gon |
| 180 ° | 200 gon |
| 270 ° | 300 gon |
| 360 ° | 400 gon |
Where it's used
Degrees are used for geometry, surveying and navigation, while gradians appear in land surveying in Europe. Both measure plane angle, so the conversion is a fixed factor.
Degree to other angle units
| Conversion | 1 ° equals |
|---|---|
| degree to gradian | 1.111111111 gon |
| degree to radian | 0.01745329252 rad |
| degree to revolution | 0.002777777778 rev |
| degree to minute of arc | 60 ′ |
| degree to second of arc | 3600 ″ |
Frequently asked questions
How many gradians are in 1 degree?
1 ° = 1.111111111 gon.
How do I convert degrees to gradians?
Multiply the value in ° by 1.111111111. For example, 15 ° × 1.111111111 = 16.66666667 gon.
Is the ° 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 Degrees to Gradians (° to gon). Retrieved October 25, 2026, from https://scientificconverters.com/angle/degrees-to-gradians/
IEEE
Scientific Converters, "Convert Degrees to Gradians (° to gon)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/degrees-to-gradians/