Convert Radians per second to Milliradians per second
Convert Radians per second (rad/s) to Milliradians per second (mrad/s) instantly and accurately.
Conversion Formula
mrad/s = rad/s × 1000
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 Milliradians per second
The milliradian per second (mrad/s) is 10⁻³ rad/s, used in precision guidance and antenna pointing. Phased-array radar beam steering rates for track-while-scan modes are typically 10-1000 mrad/s. LEO Earth-observation satellites (Sentinel-2, WorldView-3) manoeuvre between imaging targets at 5-20 mrad/s and slew at 50-200 mrad/s. Industrial robot wrist joints (KUKA, Fanuc) operate at 17-175 mrad/s. Optical encoders (Heidenhain RON 905) can measure angular velocity to 0.1 mrad/s accuracy. 1 mrad/s = 10⁻³ rad/s ≈ 0.0573 °/s ≈ 9.549 × 10⁻³ rpm.
Quick Reference Table
| Radians per second (rad/s) | Milliradians per second (mrad/s) |
|---|---|
| 1 rad/s | 1000 mrad/s |
| 2 rad/s | 2000 mrad/s |
| 5 rad/s | 5000 mrad/s |
| 10 rad/s | 10000 mrad/s |
| 25 rad/s | 25000 mrad/s |
| 50 rad/s | 50000 mrad/s |
| 100 rad/s | 100000 mrad/s |