Convert Radians per second to Revolutions per second
Convert Radians per second (rad/s) to Revolutions per second (rps) instantly and accurately.
Conversion Formula
rps = rad/s × 0.1591549431
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 Revolutions per second
The revolution per second (rps) equals 2π rad/s ≈ 6.283 rad/s = 60 rpm, used for high-speed machines where rpm values become unwieldy. Numerically equal to hertz (Hz): a 100 rps rotor produces 100 Hz unbalance vibration, directly readable on an FFT spectrum. Gas turbine HP spools (GE GEnx) operate at 100-200 rps at cruise. Ultracentrifuges (Beckman Optima MAX-XP) reach 1333 rps (80000 rpm, 600000 × g). NMR magic-angle spinning probes rotate solid samples at 5-170 rps. Dental air turbines peak at 400-800 rps. 1 rps = 2π rad/s = 60 rpm = 360 °/s.
Quick Reference Table
| Radians per second (rad/s) | Revolutions per second (rps) |
|---|---|
| 1 rad/s | 0.159155 rps |
| 2 rad/s | 0.31831 rps |
| 5 rad/s | 0.795775 rps |
| 10 rad/s | 1.59155 rps |
| 25 rad/s | 3.97887 rps |
| 50 rad/s | 7.95775 rps |
| 100 rad/s | 15.9155 rps |