Convert Radians per second to Nanoradians per second
Convert Radians per second (rad/s) to Nanoradians per second (nrad/s) instantly and accurately.
Conversion Formula
nrad/s = rad/s × 1000000000
About Radians per second
The radian per second (rad/s) is the SI coherent derived unit of angular velocity. It appears naturally in all analytical mechanics: angular frequency ω = 2πf; torque-power relation P = τω; pendulum natural frequency ωₙ = √(g/L); Bode plot frequency axis. All SI engineering software (FEM solvers, robotics middleware ROS, control system toolboxes) uses rad/s natively. Earth's rotation rate Ω⊕ = 7.292 × 10⁻⁵ rad/s. Power electronics PWM carriers at 2-20 kHz correspond to 12566-125664 rad/s. 1 rad/s ≈ 9.5493 rpm = 57.296 °/s.
About Nanoradians per second
The nanoradian per second (nrad/s) is 10⁻⁹ rad/s, accessible only to the most sensitive geodetic rotation sensors. The Wettzell G-ring laser gyroscope (4 m × 4 m Sagnac interferometer, Bavaria) measures Earth's rotation of ~72.92 µrad/s to a few nrad/s, resolving the Chandler wobble and polar motion. The proposed GINGER experiment targets the Lense-Thirring gravitomagnetic frame-dragging effect, predicted at ~39 nrad/s. State-of-the-art tactical-grade MEMS gyroscopes reach ~100 nrad/s/√Hz noise floors. 1 nrad/s = 10⁻⁹ rad/s ≈ 7.46 × 10⁻⁷ rpm.
Quick Reference Table
| Radians per second (rad/s) | Nanoradians per second (nrad/s) |
|---|---|
| 1 rad/s | 1000000000 nrad/s |
| 2 rad/s | 2 × 109 nrad/s |
| 5 rad/s | 5 × 109 nrad/s |
| 10 rad/s | 1 × 1010 nrad/s |
| 25 rad/s | 2.5 × 1010 nrad/s |
| 50 rad/s | 5 × 1010 nrad/s |
| 100 rad/s | 1 × 1011 nrad/s |