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/Second = RPM × 0.1047
Multiply any RPM value by 0.1047 to get Radian/Second.
Reverse: RPM = Radian/Second × 9.549
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rpm = 0.1047 rad/s
| RPM (rpm) | Radian/Second (rad/s) | Context |
|---|---|---|
| 0.001 rpm | 0.0001047 rad/s | Very slow |
| 0.01 rpm | 0.001047 rad/s | 10 mRPM |
| 0.1 rpm | 0.01047 rad/s | Slow rotation |
| 1 rpm | 0.1047 rad/s | 1 rpm |
| 10 rpm | 1.047 rad/s | 10 rpm |
| 60 rpm | 6.283 rad/s | 1 rps |
| 100 rpm | 10.47 rad/s | ~10.5 rad/s |
| 500 rpm | 52.36 rad/s | ~52.4 rad/s |
| 1000 rpm | 104.7 rad/s | ~104.7 rad/s |
| 1500 rpm | 157.1 rad/s | 50 Hz 4-pole motor |
| 3000 rpm | 314.2 rad/s | 50 Hz 2-pole motor |
| 7200 rpm | 754 rad/s | Hard drive |
| 1.5e+04 rpm | 1571 rad/s | F1 engine peak |
| 1e+05 rpm | 1.047e+04 rad/s | Centrifuge |
| 1e+06 rpm | 1.047e+05 rad/s | Ultra high speed |
rpm × π/30 = rad/s. Round to × 0.1047.
60 rpm = 2π rad/s. 1 rpm = 0.1047 rad/s. 3,000 rpm = 314.2 rad/s (50 Hz motor).
rad/s × 30/π = rpm.
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 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 rpm = 0.1047 rad/s. Reverse: 1 rad/s = 9.549 rpm.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.