Convert Gradians to Nanoradians
Convert Gradians (grad) to Nanoradians (nrad) instantly and accurately.
Conversion Formula
nrad = grad × 15707963.27
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.
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
| Gradians (grad) | Nanoradians (nrad) |
|---|---|
| 1 grad | 15708000 nrad |
| 2 grad | 31415900 nrad |
| 5 grad | 78539800 nrad |
| 10 grad | 157080000 nrad |
| 25 grad | 392699000 nrad |
| 50 grad | 785398000 nrad |
| 100 grad | 1.571 × 109 nrad |