Convert Semicircles to Milliradians

Convert Semicircles (sc) to Milliradians (mrad) instantly and accurately.

Conversion Formula

mrad = sc × 3141.592654

About Semicircles

A semicircle equals 1/2 of a full circle - exactly π rad = 180°. GPS and GLONASS transmit satellite orbital elements with latitude and longitude in semicircles, maximising angular resolution within 32-bit signed integers: ±2³¹ units span ±π rad with ~1.46 × 10⁻⁹ rad resolution per unit. Euler's identity e^(iπ) + 1 = 0 encodes exactly 1 semicircle of rotation in the complex plane, mapping 1 to -1 - often called the most beautiful equation in mathematics. 1 semicircle = π rad = 180° = 200 grad = 3,200 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″.

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