Reference table
Angle: degrees, radians and gon
Mathematics and physics work in radians, everyday use and engineering in degrees, surveying in gon. The table shows the same angle in every unit.
| ° | rad | gon | turn |
|---|---|---|---|
| 1 | 0.01745329 rad | 1.11111111 gon | 0.00277778 turn |
| 15 | 0.26179939 rad | 16.66666667 gon | 0.04166667 turn |
| 30 | 0.52359878 rad | 33.33333333 gon | 0.08333333 turn |
| 45 | 0.78539816 rad | 50 gon | 0.125 turn |
| 90 | 1.57079633 rad | 100 gon | 0.25 turn |
| 180 | 3.14159265 rad | 200 gon | 0.5 turn |
| 270 | 4.71238898 rad | 300 gon | 0.75 turn |
| 360 | 6.28318531 rad | 400 gon | 1 turn |
A full turn is 360° = 2π rad = 400 gon = 1 turn. The radian is dimensionless because it is a ratio of lengths, which is why formulas often state angles without a unit. Gon is used mainly in surveying, where 100 gon make a right angle.