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/Second = Revolution/Second × 6.283
Multiply any Revolution/Second value by 6.283 to get Radian/Second.
Reverse: Revolution/Second = Radian/Second × 0.1592
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rps = 6.283 rad/s
| Revolution/Second (rps) | Radian/Second (rad/s) | Context |
|---|---|---|
| 0.000167 rps | 0.001049 rad/s | 1 rpm |
| 0.001 rps | 0.006283 rad/s | 0.06 rpm |
| 0.01 rps | 0.06283 rad/s | 0.6 rpm |
| 0.1 rps | 0.6283 rad/s | 6 rpm |
| 1 rps | 6.283 rad/s | 60 rpm |
| 16.67 rps | 104.7 rad/s | 1,000 rpm |
| 50 rps | 314.2 rad/s | 3,000 rpm |
| 100 rps | 628.3 rad/s | 6,000 rpm |
| 120 rps | 754 rad/s | 7,200 rpm hard drive |
| 167 rps | 1049 rad/s | 10,000 rpm |
| 500 rps | 3142 rad/s | 30,000 rpm |
| 1000 rps | 6283 rad/s | 60,000 rpm |
| 5000 rps | 3.142e+04 rad/s | 300,000 rpm |
| 1e+04 rps | 6.283e+04 rad/s | 600,000 rpm |
| 7.16e+08 rps | 4.499e+09 rad/s | Fastest pulsar |
rps × 2π = rad/s. Exact.
1 rps = 2π rad/s ≈ 6.283 rad/s. 60 rpm = 1 rps = 6.283 rad/s.
rad/s ÷ 2π = 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.
Radian per second (rad/s) is the SI unit of angular velocity, measuring the angle swept per unit time in radians. Since 2π radians = one full rotation, 1 rps = 2π rad/s ≈ 6.283 rad/s. The unit was formalized with the SI system.
rad/s is universal in physics, control systems, and electrical engineering. Angular velocity ω relates to linear velocity v by v = ωr (r = radius). Electric motor angular speed: 50 Hz motor = 100π rad/s ≈ 314 rad/s; turbine at 3,000 rpm = 314.2 rad/s.
Interesting fact: Earth's rotation rate is about 7.27×10⁻⁵ rad/s (one revolution per 24 hours). The Milky Way rotates at about 2.7×10⁻¹⁶ rad/s — it takes about 225 million years to complete one galactic rotation.
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 = 6.283 rad/s. Reverse: 1 rad/s = 0.1592 rps.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.