Convert Revolutions per second to Radians per second

Convert Revolutions per second (rps) to Radians per second (rad/s) instantly and accurately.

Conversion Formula

rad/s = rps × 6.283185307

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.

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.

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