Convert Radians per second to Degrees per hour
Convert Radians per second (rad/s) to Degrees per hour (°/h) instantly and accurately.
Conversion Formula
°/h = rad/s × 206264.8062
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 hour
The degree per hour (°/h) equals π/648000 rad/s ≈ 4.848 × 10⁻⁶ rad/s, the universal benchmark for gyroscope drift rate. Performance tiers: consumer MEMS (smartphone) 30-2000 °/h; tactical grade (guided munitions) 0.1-30 °/h; navigation grade (commercial aircraft) 0.001-0.1 °/h; strategic grade (submarines, ICBMs) below 0.001 °/h. Earth's rotation rate of 15.041 °/h is the calibration reference for every gyrocompass. A 0.01 °/h drift yields about 1.1 km position error after 1 hour of unaided inertial navigation at the equator. 1 °/h ≈ 4.848 × 10⁻⁶ rad/s.
Quick Reference Table
| Radians per second (rad/s) | Degrees per hour (°/h) |
|---|---|
| 1 rad/s | 206265 °/h |
| 2 rad/s | 412530 °/h |
| 5 rad/s | 1031320 °/h |
| 10 rad/s | 2062650 °/h |
| 25 rad/s | 5156620 °/h |
| 50 rad/s | 10313200 °/h |
| 100 rad/s | 20626500 °/h |