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: RPM = Degree/Second × 0.1667
Multiply any Degree/Second value by 0.1667 to get RPM.
Reverse: Degree/Second = RPM × 6
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 °/s = 0.1667 rpm
| Degree/Second (°/s) | RPM (rpm) | Context |
|---|---|---|
| 0.0042 °/s | 0.0007 rpm | Earth rotation |
| 0.01 °/s | 0.001667 rpm | Very slow |
| 0.1 °/s | 0.01667 rpm | 0.017 rpm |
| 1 °/s | 0.1667 rpm | 0.167 rpm |
| 6 °/s | 1 rpm | 1 rpm |
| 57.3 °/s | 9.55 rpm | ~10 rpm |
| 180 °/s | 30 rpm | 30 rpm |
| 360 °/s | 60 rpm | 1 rps = 60 rpm |
| 1800 °/s | 300 rpm | 300 rpm |
| 3600 °/s | 600 rpm | 600 rpm |
| 1.8e+04 °/s | 3000 rpm | 3,000 rpm |
| 3.6e+04 °/s | 6000 rpm | 6,000 rpm |
| 1e+05 °/s | 1.667e+04 rpm | 16,667 rpm |
| 1e+06 °/s | 1.667e+05 rpm | Very fast |
| 1.000e+09 °/s | 1.667e+08 rpm | Extreme |
°/s ÷ 6 = rpm. Exact.
6°/s = 1 rpm. 360°/s = 60 rpm = 1 rps.
rpm × 6 = °/s.
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 minute (RPM) is the most widely used angular velocity unit for rotating machinery, engines, and motors. One RPM = 2π/60 rad/s ≈ 0.10472 rad/s. It has been used in mechanical engineering since the era of steam engines.
RPM is ubiquitous: car engines idle at 700–900 rpm, red-line at 6,000–8,000 rpm; hard drives at 5,400–7,200 rpm; centrifuges at 1,000–100,000 rpm; dental drills at 300,000–400,000 rpm; electric motors from 1 to 100,000+ rpm.
Interesting fact: The fastest spinning man-made object is a nanoscale rotor that achieved 60 billion rpm (1 GHz) in 2018. A Formula 1 engine peaks at about 15,000 rpm. A hummingbird's wings beat at about 4,000 rpm — so fast they appear as a blur.
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 = 0.1667 rpm. Reverse: 1 rpm = 6 °/s.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.