Convert Radians per second to Degrees per second
Convert Radians per second (rad/s) to Degrees per second (°/s) instantly and accurately.
Conversion Formula
°/s = rad/s × 57.29577951
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 Degrees per second
The degree per second (°/s) equals π/180 rad/s ≈ 0.01745 rad/s, the most widely used angular velocity unit in consumer electronics, robotics, and aviation. MEMS gyroscopes in smartphones range from ±16 °/s (precision mode) to ±2000 °/s (sports mode). Normal human head rotation is 30-80 °/s; car crash events exceed 2000 °/s. Weather radar antennas (WSR-88D NEXRAD) rotate at 3-6 °/s; FAA flight data recorders log roll rate to ±100 °/s. Robot joints (Universal Robots UR5e) operate at 10-180 °/s. 1 °/s = π/180 rad/s ≈ 1/6 rpm.
Quick Reference Table
| Radians per second (rad/s) | Degrees per second (°/s) |
|---|---|
| 1 rad/s | 57.2958 °/s |
| 2 rad/s | 114.592 °/s |
| 5 rad/s | 286.479 °/s |
| 10 rad/s | 572.958 °/s |
| 25 rad/s | 1432.39 °/s |
| 50 rad/s | 2864.79 °/s |
| 100 rad/s | 5729.58 °/s |