40 turn to gon — 40 turns in gradians
Exact 40 × 400 = 16,000
40 turns in other units
| Degrees | 14,400 | ° |
|---|---|---|
| Radians | 251.327412 | rad |
| Milliradians | 251,327.41 | mrad |
| Gradians | 16,000 | gon |
| Arcminutes | 864,000 | ′ |
| Arcseconds | 51,840,000 | ″ |
turn to gon at a glance
| Turns | Gradians |
|---|---|
| 1 turn | 400 gon |
| 2 turn | 800 gon |
| 3 turn | 1,200 gon |
| 5 turn | 2,000 gon |
| 10 turn | 4,000 gon |
| 20 turn | 8,000 gon |
| 25 turn | 10,000 gon |
| 50 turn | 20,000 gon |
| 100 turn | 40,000 gon |
| 250 turn | 100,000 gon |
| 500 turn | 200,000 gon |
| 1,000 turn | 400,000 gon |
How to convert turns to gradians
Multiply by 400 — one turn is 400 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 40 × 400 = 16,000
In words: sixteen thousand gradians.
Questions
How many gradians are in a turn?
One turn is 400 gradians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 40 turns in gradians?
40 turns is 16,000 gradians. The working is 40 × 400 = 16,000.
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.