Radians to gradians
Multiply radians by 63.662 to get gradians.
3 rad = 190.9859 gon
How to convert radians to gradians
The gradian is one 400th of a full turn — used in surveying. The radian is the SI angle unit — the angle subtending an arc equal to the radius; a full turn is 2π rad.
Worked example — 3 rad: 3 × 63.662 = 190.9859 gon.
Radians to gradians table
| Radians | Gradians |
|---|---|
| 0.5 rad | 31.831 gon |
| 1 rad | 63.662 gon |
| 1.5708 rad | 100.0002 gon |
| 2 rad | 127.324 gon |
| 3 rad | 190.9859 gon |
| 3.1416 rad | 200.0005 gon |
| 4 rad | 254.6479 gon |
| 5 rad | 318.3099 gon |
| 6.2832 rad | 400.0009 gon |
Reverse and related
About radians and gradians
Radian (rad)
1 rad = 63.662 gonDefinition. The SI angle unit — the angle subtending an arc equal to the radius; a full turn is 2π rad
History and origin
The radian is the natural mathematical measure of angle, the angle that cuts off an arc equal to the radius, so a full turn is 2π radians. The idea dates to the eighteenth century and the name was adopted in the 1870s.
Current use
Radians are used in trigonometry, physics and programming, where they make the mathematics of rotation simplest.
Source: BIPM SI Brochure (2019); ISO 80000-3 (angle)
Gradian (gon)
1 gon = 0.015708 radDefinition. One 400th of a full turn — used in surveying
History and origin
The gradian, or gon, divides the right angle into 100 parts, giving 400 to a full turn. It was introduced in France alongside the metric system to decimalise angle measure.
Current use
Gradians are used in surveying and some European engineering.
Source: BIPM SI Brochure (2019); ISO 80000-3 (angle)
Where people use this
Radians: trigonometry, physics, programming. Gradians: surveying, some European engineering. π radians is exactly 200 gradians.
Every value is carried to full double precision; the display is rounded.
Both units are defined in BIPM SI Brochure (2019); ISO 80000-3 (angle).
Questions people ask
How many gradians is π radians?
π radians is exactly 200 gradians.
How many gradians in a radian?
One radian is about 63.66 gradians.
How many gradians is 2π radians?
A full turn, 2π radians, is 400 gradians.