3 rad to gon — 3 radians in gradians
Exact 3 × 63.661977 = 190.985932
171 degrees 53 arcminutes 14 arcseconds
3 radians in other units
| Degrees | 171.887339 | ° |
|---|---|---|
| Milliradians | 3,000 | mrad |
| Gradians | 190.985932 | gon |
| Arcminutes | 10,313.24 | ′ |
| Arcseconds | 618,794.42 | ″ |
| Turns | 0.47746483 | turn |
rad to gon at a glance
| Radians | Gradians |
|---|---|
| 1 rad | 63.661977 gon |
| 2 rad | 127.323954 gon |
| 3 rad | 190.985932 gon |
| 5 rad | 318.309886 gon |
| 10 rad | 636.619772 gon |
| 20 rad | 1,273.24 gon |
| 25 rad | 1,591.55 gon |
| 50 rad | 3,183.1 gon |
| 100 rad | 6,366.2 gon |
| 250 rad | 15,915.49 gon |
| 500 rad | 31,830.99 gon |
| 1,000 rad | 63,661.98 gon |
How to convert radians to gradians
Multiply by 63.661977 — one radian is 63.661977 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 3 × 63.661977 = 190.985932
In words: about one hundred ninety-one gradians.
What these units are
The radian and the gradian are covered in the angle unit guide, along with every other unit on this page.
Questions
How many gradians are in a radian?
One radian is 63.661977 gradians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 3 radians in gradians?
3 radians is 190.985932 gradians. The working is 3 × 63.661977 = 190.985932.
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.