Gradians to degrees – and degrees to gradians
1 gon = 0.9 °
All units in this category
- 81°
- 1.4137167rad
- 1,413.7167mrad
- 90gon
- 4,860′
- 291,600″
- 0.225rev
Formula
Multiply the value in gradians by 0.9 to get degrees.° = gon × 0.9
Multiply the value in degrees by 1.1111111 to get gradians.gon = ° × 1.1111111
How to convert gradians to degrees
Type a value in the field above and the result is calculated instantly. Use the arrow button to swap direction, or pick other units from the lists.
Doing it in your head
A rough conversion for when the calculator is not to hand. The error comes last, and it holds in both directions at that order of magnitude.
- Degrees to gradians: × 1 + 10%. That gives 1.1 instead of 1.11111, an error of 1%.
Gradians to degrees – common values
| Gradians (gon) | Degrees (°) |
|---|---|
| 1 | 0.9 |
| 15 | 13.5 |
| 30 | 27 |
| 45 | 40.5 |
| 60 | 54 |
| 90 | 81 |
| 120 | 108 |
| 180 | 162 |
| 270 | 243 |
| 360 | 324 |
Degrees to gradians – common values
| Degrees (°) | Gradians (gon) |
|---|---|
| 1 | 1.11111 |
| 15 | 16.6667 |
| 30 | 33.3333 |
| 45 | 50 |
| 60 | 66.6667 |
| 90 | 100 |
| 120 | 133.333 |
| 180 | 200 |
| 270 | 300 |
| 360 | 400 |
About the units
Gradians. A gradian, or gon, is one 400th of a turn and therefore exactly 0.9 degrees – 100 gon make a right angle. The unit is listed among the legal units in the EU units directive, which allows prefixes on gon but not on the degree. It lives on in surveying and geodesy: the Swedish national grid is called RT 90 2.5 gon V, its central meridian lying 2.5 gon, 2.25 degrees, west of the reference meridian. The GRA mode on a calculator is gon, not degrees.
Degrees. A degree is one 360th of a turn, π/180 radians. The degree is not an SI unit, but it is one of the long-standing units of angle in the SI Brochure, and it is a legal unit throughout the EU. It is used for maps, coordinates, building angles and compass bearings. Coordinates can be written in decimal degrees, in degrees with decimal minutes or in degrees, minutes and seconds: 15.51° is 15°30.6′, that is 15°30′36″. And there is the trap: 15.51° is not 15°51′.