Convert Milliradians to Milliarcseconds

Convert Milliradians (mrad) to Milliarcseconds (mas) instantly and accurately.

Conversion Formula

mas = mrad × 206264.8062

About Milliradians

A milliradian (mrad) is one thousandth of a radian (10⁻³ rad ≈ 0.05730°). The MIL-dot reticle system in precision rifle scopes uses milliradians for its elegant property: at range R metres, 1 mrad subtends exactly R mm - so at 300 m, 1 mrad = 300 mm; at 1,000 m, 1 mrad = 1,000 mm = 1 m. Semiconductor laser slow-axis divergence is typically 5-15 mrad. Note: 1 mrad ≠ 1 NATO mil (which is π/3,200 rad ≈ 0.9817 mrad). 1 mrad ≈ 0.05730° ≈ 3.438′ ≈ 206.3″.

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.

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