Convert angular velocity units — rad/s, deg/s, RPM, RPS and more.
| Unit | Name | Value |
|---|---|---|
| °/s | Degree/Second | 57.295755 |
| rpm | Revolution/Minute | 9.5492743 |
| rps | Revolution/Second | 0.15915508 |
| rad/min | Radian/Minute | 59.9988 |
Formula: Revolution/Second = Radian/Second × 0.1592
Multiply any Radian/Second value by 0.1592 to get Revolution/Second.
Reverse: Radian/Second = Revolution/Second × 6.283
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rad/s = 0.1592 rps
| Radian/Second (rad/s) | Revolution/Second (rps) | Context |
|---|---|---|
| 7.270e-05 rad/s | 1.157e-05 rps | Earth rotation |
| 0.001 rad/s | 0.0001592 rps | Very slow |
| 0.01 rad/s | 0.001592 rps | Slow mechanism |
| 0.1 rad/s | 0.01592 rps | 0.955 rpm |
| 1 rad/s | 0.1592 rps | 9.55 rpm |
| 3.142 rad/s | 0.5 rps | π rad/s = 30 rpm |
| 6.283 rad/s | 1 rps | 1 rps = 60 rpm |
| 10 rad/s | 1.592 rps | 95.5 rpm |
| 52.36 rad/s | 8.333 rps | 500 rpm |
| 100 rad/s | 15.92 rps | 955 rpm |
| 314.2 rad/s | 50.01 rps | 3,000 rpm motor |
| 628.3 rad/s | 100 rps | 6,000 rpm |
| 1000 rad/s | 159.2 rps | 9,549 rpm |
| 1e+04 rad/s | 1592 rps | 95,490 rpm |
| 1e+06 rad/s | 1.592e+05 rps | Very high speed |
rad/s ÷ 2π = rps. Exact.
2π rad/s = 1 rps = 60 rpm. 314.2 rad/s = 50 rps.
rps × 2π = rad/s.
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 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.
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.
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/s = 0.1592 rps. Reverse: 1 rps = 6.283 rad/s.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.