Convert Quadrants to Nanoradians
Convert Quadrants (quad) to Nanoradians (nrad) instantly and accurately.
Conversion Formula
nrad = quad × 1570796327
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 Nanoradians
A nanoradian (nrad) is one billionth of a radian (10⁻⁹ rad), the smallest angle unit in regular scientific use. LIGO and Virgo gravitational-wave observatories maintain mirror tilts to sub-nanoradian stability - a 1 nrad tilt on a 4 km mirror shifts the reflected beam by 4 nm. Earth-tidal deformation deflects the local plumb line by roughly 50 nrad over a full tidal cycle, measurable with superconducting gravimeters and ring-laser gyroscopes. Synchrotron X-ray beamline mirrors are steered to single-digit nanoradians by piezo actuators. 1 nrad = 10⁻⁹ rad ≈ 0.206 µas.
Quick Reference Table
| Quadrants (quad) | Nanoradians (nrad) |
|---|---|
| 1 quad | 1.571 × 109 nrad |
| 2 quad | 3.142 × 109 nrad |
| 5 quad | 7.854 × 109 nrad |
| 10 quad | 1.571 × 1010 nrad |
| 25 quad | 3.927 × 1010 nrad |
| 50 quad | 7.854 × 1010 nrad |
| 100 quad | 1.571 × 1011 nrad |