Convert angular velocity units — rad/s, deg/s, RPM, RPS and more.
| Unit | Name | Value |
|---|---|---|
| rad/s | Radian/Second | 0.10472 |
| °/s | Degree/Second | 6.0000115 |
| rps | Revolution/Second | 0.01666672 |
| rad/min | Radian/Minute | 6.2830743 |
Formula: Radian/Minute = RPM × 6.283
Multiply any RPM value by 6.283 to get Radian/Minute.
Reverse: RPM = Radian/Minute × 0.1592
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rpm = 6.283 rad/min
| RPM (rpm) | Radian/Minute (rad/min) | Context |
|---|---|---|
| 0.001 rpm | 0.006283 rad/min | Very slow |
| 0.01 rpm | 0.06283 rad/min | 10 mRPM |
| 0.1 rpm | 0.6283 rad/min | Slow rotation |
| 1 rpm | 6.283 rad/min | 1 rpm |
| 10 rpm | 62.83 rad/min | 10 rpm |
| 60 rpm | 377 rad/min | 1 rps |
| 100 rpm | 628.3 rad/min | ~10.5 rad/s |
| 500 rpm | 3142 rad/min | ~52.4 rad/s |
| 1000 rpm | 6283 rad/min | ~104.7 rad/s |
| 1500 rpm | 9425 rad/min | 50 Hz 4-pole motor |
| 3000 rpm | 1.885e+04 rad/min | 50 Hz 2-pole motor |
| 7200 rpm | 4.524e+04 rad/min | Hard drive |
| 1.5e+04 rpm | 9.425e+04 rad/min | F1 engine peak |
| 1e+05 rpm | 6.283e+05 rad/min | Centrifuge |
| 1e+06 rpm | 6.283e+06 rad/min | Ultra high speed |
1 rpm = 6.283 rad/min.
60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s. Memorize this chain.
Multiply result by 0.1592 to recover the original rpm 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.
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.
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.
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 rpm = 6.283 rad/min. Reverse: 1 rad/min = 0.1592 rpm.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.