1,000 ″ to rad — 1,000 arcseconds in radians
Exact 1,000 ÷ 206,264.81 = 0.004848136811
16 arcminutes 40 arcseconds
1,000 arcseconds in other units
| Degrees | 0.27777778 | ° |
|---|---|---|
| Radians | 0.004848136811 | rad |
| Milliradians | 4.848137 | mrad |
| Gradians | 0.30864198 | gon |
| Arcminutes | 16.666667 | ′ |
| Turns | 0.000771604938 | turn |
″ to rad at a glance
| Arcseconds | Radians |
|---|---|
| 1 ″ | 0.000004848137 rad |
| 2 ″ | 0.000009696274 rad |
| 3 ″ | 0.00001454441 rad |
| 5 ″ | 0.000024240684 rad |
| 10 ″ | 0.000048481368 rad |
| 20 ″ | 0.000096962736 rad |
| 25 ″ | 0.00012120342 rad |
| 50 ″ | 0.000242406841 rad |
| 100 ″ | 0.000484813681 rad |
| 250 ″ | 0.001212034203 rad |
| 500 ″ | 0.002424068406 rad |
| 1,000 ″ | 0.004848136811 rad |
How to convert arcseconds to radians
Multiply by 0.000004848137 — one arcsecond is 0.000004848137 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 1,000 ÷ 206,264.81 = 0.004848136811
What these units are
The arcsecond and the radian are covered in the angle unit guide, along with every other unit on this page.
Questions
How many radians are in a arcsecond?
One arcsecond is 0.000004848137 radians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 1,000 arcseconds in radians?
1,000 arcseconds is 0.004848136811 radians. The working is 1,000 ÷ 206,264.81 = 0.004848136811.
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.