Convert angular velocity units — rad/s, deg/s, RPM, RPS and more.
| Unit | Name | Value |
|---|---|---|
| rad/s | Radian/Second | 6.28318 |
| °/s | Degree/Second | 359.99954 |
| rpm | Revolution/Minute | 59.999809 |
| rad/min | Radian/Minute | 376.98326 |
Formula: RPM = Revolution/Second × 60
Multiply any Revolution/Second value by 60 to get RPM.
Reverse: Revolution/Second = RPM × 0.01667
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rps = 60 rpm
| Revolution/Second (rps) | RPM (rpm) | Context |
|---|---|---|
| 0.000167 rps | 0.01002 rpm | 1 rpm |
| 0.001 rps | 0.06 rpm | 0.06 rpm |
| 0.01 rps | 0.6 rpm | 0.6 rpm |
| 0.1 rps | 6 rpm | 6 rpm |
| 1 rps | 60 rpm | 60 rpm |
| 16.67 rps | 1000 rpm | 1,000 rpm |
| 50 rps | 3000 rpm | 3,000 rpm |
| 100 rps | 6000 rpm | 6,000 rpm |
| 120 rps | 7200 rpm | 7,200 rpm hard drive |
| 167 rps | 1.002e+04 rpm | 10,000 rpm |
| 500 rps | 3e+04 rpm | 30,000 rpm |
| 1000 rps | 6e+04 rpm | 60,000 rpm |
| 5000 rps | 3e+05 rpm | 300,000 rpm |
| 1e+04 rps | 6e+05 rpm | 600,000 rpm |
| 7.16e+08 rps | 4.296e+10 rpm | Fastest pulsar |
rps × 60 = rpm. Exact.
1 rps = 60 rpm = 2π rad/s ≈ 6.283 rad/s.
rpm ÷ 60 = rps.
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 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.
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 rps = 60 rpm. Reverse: 1 rpm = 0.01667 rps.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.