Convert Revolutions per minute to Radians per second
Convert Revolutions per minute (rpm) to Radians per second (rad/s) instantly and accurately.
Conversion Formula
rad/s = rpm × 0.1047197551
About Revolutions per minute
The revolution per minute (rpm) equals π/30 rad/s ≈ 0.1047 rad/s, the most universally recognised rotational speed unit in mechanical engineering. Common references: car petrol engines idle at 600-900 rpm, redline at 5500-8500 rpm; large marine diesel engines run at 75-120 rpm; electric induction motor synchronous speed = 60f/p rpm (3000 rpm at 50 Hz, 2-pole); hard drives at 5400-15000 rpm; dental turbines up to 400000 rpm; washing machine spin 400-1600 rpm. ISO 6336 and ANSI/AGMA gear standards use rpm throughout. 1 rpm = π/30 rad/s = 6 °/s = 1/60 rps.
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.
Quick Reference Table
| Revolutions per minute (rpm) | Radians per second (rad/s) |
|---|---|
| 1 rpm | 0.10472 rad/s |
| 2 rpm | 0.20944 rad/s |
| 5 rpm | 0.523599 rad/s |
| 10 rpm | 1.0472 rad/s |
| 25 rpm | 2.61799 rad/s |
| 50 rpm | 5.23599 rad/s |
| 100 rpm | 10.472 rad/s |