Convert Signs to Milliradians

Convert Signs (sign) to Milliradians (mrad) instantly and accurately.

Conversion Formula

mrad = sign × 523.5987756

About Signs

An astrological sign equals 1/12 of a full circle - π/6 rad = exactly 30°. The zodiac divides the ecliptic into twelve 30° signs (Aries through Pisces), originating in Babylonian astronomy ~5th century BCE. Historical ecliptic longitude was expressed as sign + degrees: "Scorpio 12°" = 222°. The 30° spacing also appears in music theory: the circle of fifths has twelve equally spaced positions 30° apart, and the octave divides into 12 equal semitones. 1 sign = 30° = 1,800′ = π/6 rad = 533.3 NATO mils.

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″.

Quick Reference Table

→ Full Angle Converter