30 ′ to rad — 30 arcminutes in radians
Exact 30 ÷ 3,437.75 = 0.00872664626
30 arcminutes in other units
| Degrees | 0.5 | ° |
|---|---|---|
| Radians | 0.00872664626 | rad |
| Milliradians | 8.726646 | mrad |
| Gradians | 0.55555556 | gon |
| Arcseconds | 1,800 | ″ |
| Turns | 0.001388888889 | turn |
′ to rad at a glance
| Arcminutes | Radians |
|---|---|
| 1 ′ | 0.000290888209 rad |
| 2 ′ | 0.000581776417 rad |
| 3 ′ | 0.000872664626 rad |
| 5 ′ | 0.001454441043 rad |
| 10 ′ | 0.002908882087 rad |
| 20 ′ | 0.005817764173 rad |
| 25 ′ | 0.007272205217 rad |
| 50 ′ | 0.01454441 rad |
| 100 ′ | 0.02908882 rad |
| 250 ′ | 0.07272205 rad |
| 500 ′ | 0.1454441 rad |
| 1,000 ′ | 0.29088821 rad |
How to convert arcminutes to radians
Multiply by 0.000290888209 — one arcminute is 0.000290888209 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 30 ÷ 3,437.75 = 0.00872664626
Questions
How many radians are in a arcminute?
One arcminute is 0.000290888209 radians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 30 arcminutes in radians?
30 arcminutes is 0.00872664626 radians. The working is 30 ÷ 3,437.75 = 0.00872664626.
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.