Convert angular velocity units — rad/s, deg/s, RPM, RPS and more.
| Unit | Name | Value |
|---|---|---|
| rad/s | Radian/Second | 0.016667 |
| °/s | Degree/Second | 0.95494835 |
| rpm | Revolution/Minute | 0.15915775 |
| rps | Revolution/Second | 0.0026526377 |
Formula: Revolution/Second = Degree/Second × 0.002778
Multiply any Degree/Second value by 0.002778 to get Revolution/Second.
Reverse: Degree/Second = Revolution/Second × 360
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 °/s = 0.002778 rps
| Degree/Second (°/s) | Revolution/Second (rps) | Context |
|---|---|---|
| 0.0042 °/s | 1.167e-05 rps | Earth rotation |
| 0.01 °/s | 2.778e-05 rps | Very slow |
| 0.1 °/s | 0.0002778 rps | 0.017 rpm |
| 1 °/s | 0.002778 rps | 0.167 rpm |
| 6 °/s | 0.01667 rps | 1 rpm |
| 57.3 °/s | 0.1592 rps | ~10 rpm |
| 180 °/s | 0.5 rps | 30 rpm |
| 360 °/s | 1 rps | 1 rps = 60 rpm |
| 1800 °/s | 5 rps | 300 rpm |
| 3600 °/s | 10 rps | 600 rpm |
| 1.8e+04 °/s | 50 rps | 3,000 rpm |
| 3.6e+04 °/s | 100 rps | 6,000 rpm |
| 1e+05 °/s | 277.8 rps | 16,667 rpm |
| 1e+06 °/s | 2778 rps | Very fast |
| 1.000e+09 °/s | 2.778e+06 rps | Extreme |
1 °/s = 0.002778 rps.
60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s. Memorize this chain.
Multiply result by 360 to recover the original °/s value.
Converts motor speed between rpm and rad/s for torque, power, and control system calculations.
Specifies joint angular velocity in °/s or rad/s for trajectory planning and servo control.
Converts between rpm and rad/s for gear ratio, centrifugal force, and bearing life calculations.
Uses rad/s for bandwidth, frequency response, and PID controller angular velocity specifications.
Calculates attitude rates in °/s and gyroscope outputs in rad/s for inertial navigation systems.
Converts Earth and celestial body rotation rates between rad/s, °/s, and rpm for orbital calculations.
Degree per second (°/s) measures angular velocity in degrees per unit time. One full revolution = 360°/s, so 1°/s = π/180 rad/s ≈ 0.01745 rad/s. It is widely used in navigation, robotics, and human motion analysis where degree values are more intuitive.
°/s is used in gyroscope specifications, aircraft attitude rates, and game controller sensitivity. MEMS gyroscopes in smartphones typically measure ±250 to ±2,000 °/s. Aircraft maximum roll rate is typically 30–200 °/s. Robotic joint speeds are often specified in °/s.
Interesting fact: Fighter pilots experience angular accelerations up to 400°/s² during high-g maneuvers. The human vestibular system can detect angular velocities as low as 0.5°/s and accelerations as low as 0.1°/s² — making it a remarkably sensitive gyroscope.
Revolutions per second (rps) equals 2π rad/s ≈ 6.2832 rad/s and is numerically identical to Hz for periodic motion. It is used in precision mechanics, turbomachinery, and electrical engineering where per-second rates are more convenient than per-minute.
rps is used for high-speed applications: a hard drive at 7,200 rpm = 120 rps; a jet turbine at 30,000 rpm = 500 rps; NMR spinning samples at 10,000–70,000 rpm = 167–1,167 rps. The unit makes angular-to-linear velocity calculations cleaner.
Interesting fact: Pulsars — rapidly rotating neutron stars — spin at up to 716 rps (the fastest known). The pulsar PSR J1748-2446ad completes 716 full rotations every second, with its equator moving at approximately 24% of the speed of light.
Angular velocity measures how fast something rotates. The SI unit is rad/s; mechanical engineering uses rpm; robotics uses °/s; power engineering converts between rpm and rad/s. Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s.
Exact factor: 1 °/s = 0.002778 rps. Reverse: 1 rps = 360 °/s.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.