Convert Quadrants to Microradians

Convert Quadrants (quad) to Microradians (µrad) instantly and accurately.

Conversion Formula

µrad = quad × 1570796.327

About Quadrants

A quadrant equals 1/4 of a full circle - π/2 rad = 90°, the right angle. Perpendicularity underpins Euclidean geometry, the Pythagorean theorem, and Cartesian coordinate systems. In AC electrical engineering, voltage and current in purely reactive circuits are exactly 90° out of phase, defining reactive power in VAr. The four quadrants of the unit circle determine the sign of sine, cosine, and tangent. GPS orbital elements encode latitude in semicircles bounded by ±1 quadrant = ±90°. 1 quadrant = 90° = 100 grad = π/2 rad = 1,600 NATO mils.

About Microradians

A microradian (µrad) is one millionth of a radian (10⁻⁶ rad ≈ 0.206265 arcseconds). It is the standard unit for small angles in precision optics and structural monitoring. A 1 µm wavelength beam from a 1 mm aperture has a diffraction-limited half-angle divergence of ~1 µrad. Atmospheric seeing for ground-based telescopes is typically 2.4-9.7 µrad (0.5-2 arcseconds). Autocollimators resolve angular deviations to 0.05-1 µrad for machine tool alignment. Building tilt monitoring tracks µrad/day. 1 µrad ≈ 0.2063″ = 0.2063 arcseconds.

Quick Reference Table

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