Convert Gradians to Radians (gon to rad)
1 gradian (gon) = 0.01570796327 radians (rad). 1 rad = 63.66197724 gon. Example: 15 gon = 15 × 0.01570796327 = 0.235619449 rad.
Also searched as gradians to rad, gradians in rad, gradians into radians, gon to rad, gon in radians, gon into radian, gradian to radian, gon to radians converter and how many radians in a gradian.
1 gon = 0.01570796327 rad
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk gradian to radian converter to paste a column from Excel.
How to Convert Gradian to Radian
- 1 gon = 0.01570796327 rad
- 1 rad = 63.66197724 gon
- Example: convert 15 gon to rad: 15 gon = 15 × 0.01570796327 rad = 0.235619449 rad
Formula
rad = gon × 0.01570796326795
or rad = gon ÷ 63.66197723676
Derivation from SI units:
- 1 gon = π/200 rad; a right angle is 100 gon and a full turn 400 gon.
- 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).
Both units are defined exactly, so the factor is exact. Gradian definition: gradian; Radian definition: radian.
Worked examples
- A reading of 50 gon converts to 0.7853981634 rad.
50 gon × 0.01570796327 = 0.7853981634 rad - A value of 200 gon is 3.141592654 rad.
200 gon × 0.01570796327 = 3.141592654 rad
Gradian to Radian conversion table
| Gradians (gon) | Radians (rad) |
|---|---|
| 1 gon | 0.01570796327 rad |
| 10 gon | 0.1570796327 rad |
| 25 gon | 0.3926990817 rad |
| 50 gon | 0.7853981634 rad |
| 100 gon | 1.570796327 rad |
| 150 gon | 2.35619449 rad |
| 200 gon | 3.141592654 rad |
| 300 gon | 4.71238898 rad |
| 400 gon | 6.283185307 rad |
| 0.5 gon | 0.007853981634 rad |
Where it's used
Gradians are used for land surveying in Europe, while radians appear in trigonometry and calculus (derivatives of sin and cos assume radians). Both measure plane angle, so the conversion is a fixed factor.
Gradian to other angle units
| Conversion | 1 gon equals |
|---|---|
| gradian to radian | 0.01570796327 rad |
| gradian to degree | 0.9 ° |
| gradian to revolution | 0.0025 rev |
| gradian to minute of arc | 54 ′ |
| gradian to second of arc | 3240 ″ |
Frequently asked questions
How many radians are in 1 gradian?
1 gon = 0.01570796327 rad.
How do I convert gradians to radians?
Multiply the value in gon by 0.01570796327, or divide it by 63.66197724. For example, 15 gon × 0.01570796327 = 0.235619449 rad.
Is the gon to rad 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 Radians (gon to rad). Retrieved October 25, 2026, from https://scientificconverters.com/angle/gradians-to-radians/
IEEE
Scientific Converters, "Convert Gradians to Radians (gon to rad)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/gradians-to-radians/