Radians to Arcminutes Converter
Convert angle measurements from radians (rad) to arcminutes ('). One radian equals approximately 3437.75 arcminutes.
radians (rad)
Result
0'
Common Radians to Arcminutes Conversions
| Radians (rad) | Arcminutes (') |
|---|---|
| 0.001 rad | 3.438' |
| 0.01 rad | 34.38' |
| 0.1 rad | 343.77' |
| π/6 (0.5236) rad | 1800' (30°) |
| π/4 (0.7854) rad | 2700' (45°) |
| 1 rad | 3437.75' |
| π/2 (1.5708) rad | 5400' (90°) |
| π (3.14159) rad | 10800' (180°) |
How to Convert Radians to Arcminutes
An arcminute is 1/60 of a degree. To convert radians to arcminutes, multiply by 10800/π (since there are 10,800 arcminutes in π radians).
The Conversion Formula
arcminutes = radians × (10800 / π)
This can also be written as: arcminutes = radians × 3437.746771
Understanding the Conversion
The conversion factor comes from: 1 radian = 180/π degrees, and 1 degree = 60 arcminutes. Therefore: 1 radian = (180/π) × 60 = 10800/π arcminutes ≈ 3437.75 arcminutes.
Example: Converting 1 Radian to Arcminutes
arcminutes = 1 rad × (10800 / π) = 1 × 3437.746771 = 3437.75'
Note: 1 radian ≈ 57.2958° ≈ 3437.75 arcminutes
Why Use Arcminutes?
Arcminutes provide a convenient way to express small angles without using decimals of degrees:
- Astronomy: Angular sizes of celestial objects (the Moon is about 31')
- Navigation: One arcminute of latitude equals one nautical mile
- Optics: Angular resolution of telescopes and cameras
- Surveying: Precise angular measurements