Convert Radians to Nanoradians
Convert Radians (rad) to Nanoradians (nrad) instantly and accurately.
Conversion Formula
nrad = rad × 1000000000
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″.
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
| Radians (rad) | Nanoradians (nrad) |
|---|---|
| 1 rad | 1000000000 nrad |
| 2 rad | 2 × 109 nrad |
| 5 rad | 5 × 109 nrad |
| 10 rad | 1 × 1010 nrad |
| 25 rad | 2.5 × 1010 nrad |
| 50 rad | 5 × 1010 nrad |
| 100 rad | 1 × 1011 nrad |