Convert Radians to Milliarcseconds
Convert Radians (rad) to Milliarcseconds (mas) instantly and accurately.
Conversion Formula
mas = rad × 206264806.2
About Radians
The radian (rad) is the SI unit of plane angle, defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle = 2π rad; a right angle = π/2 rad. The radian is dimensionless (arc length / radius), so it can be omitted in equations. All calculus and physics formulas are simplest in radians: d/dx(sin x) = cos x holds only in radians; Taylor series sin x = x − x³/6 + x⁵/120 hold only for x in radians; angular frequency ω = 2πf gives energy E = ħω. 1 rad = 180°/π ≈ 57.2958° ≈ 206,264.8″.
About Milliarcseconds
A milliarcsecond (mas) is one thousandth of an arcsecond - approximately 4.848 × 10⁻⁹ rad. It is the standard unit of precision astrometry. The ESA Hipparcos satellite measured stellar positions to ~1 mas; its successor Gaia achieves 7-100 µas for bright stars. A parallax of 1 mas corresponds to a distance of 1 kiloparsec (3,260 light-years). Very Long Baseline Interferometry (VLBI) resolves well below 1 mas, imaging structures around supermassive black holes. 1 mas = 10⁻³ arcseconds ≈ 4.848 × 10⁻⁹ rad.
Quick Reference Table
| Radians (rad) | Milliarcseconds (mas) |
|---|---|
| 1 rad | 206265000 mas |
| 2 rad | 412530000 mas |
| 5 rad | 1.031 × 109 mas |
| 10 rad | 2.063 × 109 mas |
| 25 rad | 5.157 × 109 mas |
| 50 rad | 1.031 × 1010 mas |
| 100 rad | 2.063 × 1010 mas |