Convert Gradians to Degrees (gon to °)
1 gradian (gon) = 0.9 degrees (°). 1 ° = 1.111111111 gon. Example: 15 gon = 15 × 0.9 = 13.5 °.
Also searched as gradians to °, gradians in °, gradians into degrees, gon to °, gon in degrees, gon into degree, gradian to degree, gon to degrees converter and how many degrees in a gradian.
1 gon = 0.9 °
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk gradian to degree converter to paste a column from Excel.
How to Convert Gradian to Degree
- 1 gon = 0.9 °
- 1 ° = 1.111111111 gon
- Example: convert 15 gon to °: 15 gon = 15 × 0.9 ° = 13.5 °
Formula
° = gon × 0.9
or ° = gon ÷ 1.111111111111
Derivation from SI units:
- 1 gon = π/200 rad; a right angle is 100 gon and a full turn 400 gon.
- 1° = π/180 rad exactly; a full turn is 360°.
- 1 gon = 0.01570796326795 rad ÷ 0.01745329251994 rad per ° = 0.9 °
Both units are defined exactly, so the factor is exact. Gradian definition: gradian; Degree definition: degree.
Worked examples
- A reading of 50 gon converts to 45 °.
50 gon × 0.9 = 45 ° - A value of 200 gon is 180 °.
200 gon × 0.9 = 180 °
Gradian to Degree conversion table
| Gradians (gon) | Degrees (°) |
|---|---|
| 1 gon | 0.9 ° |
| 10 gon | 9 ° |
| 25 gon | 22.5 ° |
| 50 gon | 45 ° |
| 100 gon | 90 ° |
| 150 gon | 135 ° |
| 200 gon | 180 ° |
| 300 gon | 270 ° |
| 400 gon | 360 ° |
| 0.5 gon | 0.45 ° |
Where it's used
Gradians are used for land surveying in Europe, while degrees appear in geometry, surveying and navigation. Both measure plane angle, so the conversion is a fixed factor.
Gradian to other angle units
| Conversion | 1 gon equals |
|---|---|
| gradian to degree | 0.9 ° |
| gradian to radian | 0.01570796327 rad |
| gradian to revolution | 0.0025 rev |
| gradian to minute of arc | 54 ′ |
| gradian to second of arc | 3240 ″ |
Frequently asked questions
How many degrees are in 1 gradian?
1 gon = 0.9 °.
How do I convert gradians to degrees?
Multiply the value in gon by 0.9, or divide it by 1.111111111. For example, 15 gon × 0.9 = 13.5 °.
Is the gon to ° 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
- 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".
- 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).
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 Gradians to Degrees (gon to °). Retrieved October 25, 2026, from https://scientificconverters.com/angle/gradians-to-degrees/
IEEE
Scientific Converters, "Convert Gradians to Degrees (gon to °)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/gradians-to-degrees/