Convert Arcminutes to Milliradians

Convert Arcminutes (′) to Milliradians (mrad) instantly and accurately.

Conversion Formula

mrad = ′ × 0.2908882087

About Arcminutes

An arcminute (′) is 1/60 of a degree - π/10,800 rad ≈ 2.909 × 10⁻⁴ rad. One arcminute of latitude equals exactly one nautical mile (1,852 m), which is the origin of the nautical mile unit. The Moon and Sun both subtend ~30 arcminutes in apparent diameter - the coincidence exploited in total solar eclipses. Human 20/20 visual acuity resolves letters 5 arcminutes tall at 6 m. Binocular and telescope apparent fields of view are quoted in arcminutes. 1′ = π/10,800 rad ≈ 0.01667° ≈ 290.9 µrad.

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″.

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