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 = Radian/Minute × 0.1592
Multiply any Radian/Minute value by 0.1592 to get RPM.
Reverse: Radian/Minute = RPM × 6.283
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rad/min = 0.1592 rpm
| Radian/Minute (rad/min) | RPM (rpm) | Context |
|---|---|---|
| 0.00436 rad/min | 0.0006939 rpm | Earth rotation |
| 0.01 rad/min | 0.001592 rpm | Very slow |
| 0.1 rad/min | 0.01592 rpm | ~0.955 rpm |
| 1 rad/min | 0.1592 rpm | ~9.55 rpm |
| 6.283 rad/min | 1 rpm | 1 rpm |
| 10 rad/min | 1.592 rpm | ~95.5 rpm |
| 60 rad/min | 9.549 rpm | 1 rad/s |
| 100 rad/min | 15.92 rpm | ~955 rpm |
| 600 rad/min | 95.49 rpm | ~5,730 rpm |
| 1000 rad/min | 159.2 rpm | ~9,549 rpm |
| 6283 rad/min | 1000 rpm | 1,000 rpm |
| 1e+04 rad/min | 1592 rpm | ~16 krpm |
| 1e+05 rad/min | 1.592e+04 rpm | ~160 krpm |
| 1e+06 rad/min | 1.592e+05 rpm | Very fast |
| 1.000e+09 rad/min | 1.592e+08 rpm | Extreme |
1 rad/min = 0.1592 rpm.
60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s. Memorize this chain.
Multiply result by 6.283 to recover the original rad/min 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.
Radian per minute (rad/min) equals 1/60 rad/s and is used for slow rotations in industrial processes, telescope tracking, and clock mechanisms where per-second rates would be too small. 60 rad/min = 1 rad/s; 2π rad/min ≈ 1 rpm.
Telescope mounts track celestial objects at about 0.0042 rad/min (compensating for Earth's rotation). Slow industrial mixers and stirrers operate at 1–30 rad/min. Clock minute hands rotate at 2π rad/hr = π/30 rad/min ≈ 0.105 rad/min.
Interesting fact: The minute hand of a clock rotates at exactly π/30 rad/min = 2π rad/hour. The hour hand rotates at π/360 rad/min = 2π rad/12 hours. The second hand at 2π rad/min = 1 rps = 6°/s — the only hand with a speed convenient to express in multiple units.
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 rad/min = 0.1592 rpm. Reverse: 1 rpm = 6.283 rad/min.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.