2 gon to rad — 2 gradians in radians
Exact 2 ÷ 63.661977 = 0.03141593
1 degree 48 arcminutes
2 gradians in other units
| Degrees | 1.8 | ° |
|---|---|---|
| Radians | 0.03141593 | rad |
| Milliradians | 31.415927 | mrad |
| Arcminutes | 108 | ′ |
| Arcseconds | 6,480 | ″ |
| Turns | 0.005 | turn |
gon to rad at a glance
| Gradians | Radians |
|---|---|
| 1 gon | 0.01570796 rad |
| 2 gon | 0.03141593 rad |
| 3 gon | 0.04712389 rad |
| 5 gon | 0.07853982 rad |
| 10 gon | 0.15707963 rad |
| 20 gon | 0.31415927 rad |
| 25 gon | 0.39269908 rad |
| 50 gon | 0.78539816 rad |
| 100 gon | 1.570796 rad |
| 250 gon | 3.926991 rad |
| 500 gon | 7.853982 rad |
| 1,000 gon | 15.707963 rad |
How to convert gradians to radians
Multiply by 0.01570796 — one gradian is 0.01570796 radians. 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 2 ÷ 63.661977 = 0.03141593
Questions
How many radians are in a gradian?
One gradian is 0.01570796 radians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 2 gradians in radians?
2 gradians is 0.03141593 radians. The working is 2 ÷ 63.661977 = 0.03141593.
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.