Convert Gradians to Milliarcseconds
Convert Gradians (grad) to Milliarcseconds (mas) instantly and accurately.
Conversion Formula
mas = grad × 3240000
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.
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
| Gradians (grad) | Milliarcseconds (mas) |
|---|---|
| 1 grad | 3240000 mas |
| 2 grad | 6480000 mas |
| 5 grad | 16200000 mas |
| 10 grad | 32400000 mas |
| 25 grad | 81000000 mas |
| 50 grad | 162000000 mas |
| 100 grad | 324000000 mas |