Convert Turns to Nanoradians
Convert Turns (rev) to Nanoradians (nrad) instantly and accurately.
Conversion Formula
nrad = rev × 6283185307
About Turns
A turn (revolution, cycle) equals one complete rotation - 2π rad = 360° = 400 grad. Rotational speed is naturally measured in turns per minute (rpm): a car engine idles at ~750 rpm; a hard disk spins at 7,200 rpm. The factor 2π in physics formulas (ω = 2πf, E = hf = ħω) arises from converting turns to radians. The turn is the natural unit for gear ratios, transformer winding counts, and thread pitch (turns per inch). The tau convention (τ = 2π ≈ 6.2832) proposes 1τ = 1 full turn. 1 rpm = 1/60 Hz = 2π/60 rad/s ≈ 0.10472 rad/s.
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
| Turns (rev) | Nanoradians (nrad) |
|---|---|
| 1 rev | 6.283 × 109 nrad |
| 2 rev | 1.257 × 1010 nrad |
| 5 rev | 3.142 × 1010 nrad |
| 10 rev | 6.283 × 1010 nrad |
| 25 rev | 1.571 × 1011 nrad |
| 50 rev | 3.142 × 1011 nrad |
| 100 rev | 6.283 × 1011 nrad |