Convert Nanoradians to Gradians
Convert Nanoradians (nrad) to Gradians (grad) instantly and accurately.
Conversion Formula
grad = nrad × 6.366197724e-8
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.
About Gradians
A gradian (grad), also called a gon (ISO 31/DIN), equals 1/400 of a full circle - π/200 rad = 0.9°. Its main advantage: a right angle = exactly 100 grad, simplifying complementary and supplementary angle arithmetic. Introduced during the French Revolution as part of decimal angle reform. Surveying in France, the Netherlands, Switzerland, and Scandinavia uses gradians; professional total stations display both degrees and gons. A 1% slope ≈ 0.6366 grad. 1 grad = 0.9° = 54′ = π/200 rad; 400 grad = 360° = one full circle.
Quick Reference Table
| Nanoradians (nrad) | Gradians (grad) |
|---|---|
| 1 nrad | 6.366 × 10-8 grad |
| 2 nrad | 1.273 × 10-7 grad |
| 5 nrad | 3.183 × 10-7 grad |
| 10 nrad | 6.366 × 10-7 grad |
| 25 nrad | 1.592 × 10-6 grad |
| 50 nrad | 3.183 × 10-6 grad |
| 100 nrad | 6.366 × 10-6 grad |