100 gon to ° — 100 gradians in degrees
Exact 100 ÷ 1.111111 = 90
100 gradians in other units
| Degrees | 90 | ° |
|---|---|---|
| Radians | 1.570796 | rad |
| Milliradians | 1,570.8 | mrad |
| Arcminutes | 5,400 | ′ |
| Arcseconds | 324,000 | ″ |
| Turns | 0.25 | turn |
gon to ° at a glance
| Gradians | Degrees |
|---|---|
| 1 gon | 0.9 ° |
| 2 gon | 1.8 ° |
| 3 gon | 2.7 ° |
| 5 gon | 4.5 ° |
| 10 gon | 9 ° |
| 20 gon | 18 ° |
| 25 gon | 22.5 ° |
| 50 gon | 45 ° |
| 100 gon | 90 ° |
| 250 gon | 225 ° |
| 500 gon | 450 ° |
| 1,000 gon | 900 ° |
How to convert gradians to degrees
Multiply by 0.9 — one gradian is 0.9 degrees. That factor is exact: it comes from the definition of the units rather than from a measurement, so it will not change and does not need rounding.
Working 100 ÷ 1.111111 = 90
In words: ninety degrees.
What these units are
The gradian and the degree are covered in the angle unit guide, along with every other unit on this page.
Questions
How many degrees are in a gradian?
One gradian is 0.9 degrees. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 100 gradians in degrees?
100 gradians is 90 degrees. The working is 100 ÷ 1.111111 = 90.
How many degrees is one radian?
About 57.3°, or exactly 180/π. A radian is the angle you get when the arc along a circle is as long as its radius, which is why the number is awkward: it comes from the geometry rather than from someone choosing a round figure.
Why does maths use radians instead of degrees?
Because the calculus only comes out clean in radians. The derivative of sine is cosine only when the angle is in radians; in degrees a factor of π/180 turns up everywhere. Degrees are a human convention, radians are the circle's own unit.
Why 360 degrees in a circle?
Babylonian arithmetic, most likely, and it stuck because 360 divides so willingly — by 2, 3, 4, 5, 6, 8, 9, 10, 12 and more. Halves, thirds and quarters of a circle all land on whole numbers, which is more than can be said for 100.
What is a gradian for?
It is the metric attempt at angle: 100 gradians in a right angle, 400 in a full circle. It never displaced the degree in general use but survives in surveying in parts of Europe, and most scientific calculators still have a GRAD mode next to DEG and RAD.