Convert Microradians to Radians
Convert Microradians (µrad) to Radians (rad) instantly and accurately.
Conversion Formula
rad = µrad × 1.000000000e-6
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.
About Radians
The radian (rad) is the SI unit of plane angle, defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle = 2π rad; a right angle = π/2 rad. The radian is dimensionless (arc length / radius), so it can be omitted in equations. All calculus and physics formulas are simplest in radians: d/dx(sin x) = cos x holds only in radians; Taylor series sin x = x − x³/6 + x⁵/120 hold only for x in radians; angular frequency ω = 2πf gives energy E = ħω. 1 rad = 180°/π ≈ 57.2958° ≈ 206,264.8″.
Quick Reference Table
| Microradians (µrad) | Radians (rad) |
|---|---|
| 1 µrad | 1 × 10-6 rad |
| 2 µrad | 2 × 10-6 rad |
| 5 µrad | 5 × 10-6 rad |
| 10 µrad | 1 × 10-5 rad |
| 25 µrad | 2.5 × 10-5 rad |
| 50 µrad | 5 × 10-5 rad |
| 100 µrad | 1 × 10-4 rad |