30 ° to gon — 30 degrees in gradians
Exact 30 × 1.111111 = 33.333333
30 degrees in other units
| Radians | 0.52359878 | rad |
|---|---|---|
| Milliradians | 523.598776 | mrad |
| Gradians | 33.333333 | gon |
| Arcminutes | 1,800 | ′ |
| Arcseconds | 108,000 | ″ |
| Turns | 0.08333333 | turn |
° to gon at a glance
| Degrees | Gradians |
|---|---|
| 1 ° | 1.111111 gon |
| 2 ° | 2.222222 gon |
| 3 ° | 3.333333 gon |
| 5 ° | 5.555556 gon |
| 10 ° | 11.111111 gon |
| 20 ° | 22.222222 gon |
| 25 ° | 27.777778 gon |
| 50 ° | 55.555556 gon |
| 100 ° | 111.111111 gon |
| 250 ° | 277.777778 gon |
| 500 ° | 555.555556 gon |
| 1,000 ° | 1,111.11 gon |
How to convert degrees to gradians
Multiply by 1.111111 — one degree is 1.111111 gradians. 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 30 × 1.111111 = 33.333333
In words: about thirty-three gradians.
Questions
How many gradians are in a degree?
One degree is 1.111111 gradians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 30 degrees in gradians?
30 degrees is 33.333333 gradians. The working is 30 × 1.111111 = 33.333333.
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.