Convert Semicircles to Nanoradians
Convert Semicircles (sc) to Nanoradians (nrad) instantly and accurately.
Conversion Formula
nrad = sc × 3141592654
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 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
| Semicircles (sc) | Nanoradians (nrad) |
|---|---|
| 1 sc | 3.142 × 109 nrad |
| 2 sc | 6.283 × 109 nrad |
| 5 sc | 1.571 × 1010 nrad |
| 10 sc | 3.142 × 1010 nrad |
| 25 sc | 7.854 × 1010 nrad |
| 50 sc | 1.571 × 1011 nrad |
| 100 sc | 3.142 × 1011 nrad |