Convert Milliarcseconds to Gradians
Convert Milliarcseconds (mas) to Gradians (grad) instantly and accurately.
Conversion Formula
grad = mas × 3.086419753e-7
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.
About Gradians
A gradian (grad), also called a gon (ISO 31/DIN), equals 1/400 of a full circle - π/200 rad = 0.9°. Its main advantage: a right angle = exactly 100 grad, simplifying complementary and supplementary angle arithmetic. Introduced during the French Revolution as part of decimal angle reform. Surveying in France, the Netherlands, Switzerland, and Scandinavia uses gradians; professional total stations display both degrees and gons. A 1% slope ≈ 0.6366 grad. 1 grad = 0.9° = 54′ = π/200 rad; 400 grad = 360° = one full circle.
Quick Reference Table
| Milliarcseconds (mas) | Gradians (grad) |
|---|---|
| 1 mas | 3.086 × 10-7 grad |
| 2 mas | 6.173 × 10-7 grad |
| 5 mas | 1.543 × 10-6 grad |
| 10 mas | 3.086 × 10-6 grad |
| 25 mas | 7.716 × 10-6 grad |
| 50 mas | 1.543 × 10-5 grad |
| 100 mas | 3.086 × 10-5 grad |