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: Radian/Minute = Revolution/Second × 377
Multiply any Revolution/Second value by 377 to get Radian/Minute.
Reverse: Revolution/Second = Radian/Minute × 0.002653
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rps = 377 rad/min
| Revolution/Second (rps) | Radian/Minute (rad/min) | Context |
|---|---|---|
| 0.000167 rps | 0.06296 rad/min | 1 rpm |
| 0.001 rps | 0.377 rad/min | 0.06 rpm |
| 0.01 rps | 3.77 rad/min | 0.6 rpm |
| 0.1 rps | 37.7 rad/min | 6 rpm |
| 1 rps | 377 rad/min | 60 rpm |
| 16.67 rps | 6284 rad/min | 1,000 rpm |
| 50 rps | 1.885e+04 rad/min | 3,000 rpm |
| 100 rps | 3.77e+04 rad/min | 6,000 rpm |
| 120 rps | 4.524e+04 rad/min | 7,200 rpm hard drive |
| 167 rps | 6.296e+04 rad/min | 10,000 rpm |
| 500 rps | 1.885e+05 rad/min | 30,000 rpm |
| 1000 rps | 3.77e+05 rad/min | 60,000 rpm |
| 5000 rps | 1.885e+06 rad/min | 300,000 rpm |
| 1e+04 rps | 3.77e+06 rad/min | 600,000 rpm |
| 7.16e+08 rps | 2.699e+11 rad/min | Fastest pulsar |
1 rps = 377 rad/min.
60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s. Memorize this chain.
Multiply result by 0.002653 to recover the original rps 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 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.
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 rps = 377 rad/min. Reverse: 1 rad/min = 0.002653 rps.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.