Convert angular velocity units — rad/s, deg/s, RPM, RPS and more.
| Unit | Name | Value |
|---|---|---|
| rad/s | Radian/Second | 0.0174533 |
| rpm | Revolution/Minute | 0.16666635 |
| rps | Revolution/Second | 0.0027777813 |
| rad/min | Radian/Minute | 1.0471771 |
Formula: RPM = Radian/Second × 9.549
Multiply any Radian/Second value by 9.549 to get RPM.
Reverse: Radian/Second = RPM × 0.1047
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rad/s = 9.549 rpm
| Radian/Second (rad/s) | RPM (rpm) | Context |
|---|---|---|
| 7.270e-05 rad/s | 0.0006942 rpm | Earth rotation |
| 0.001 rad/s | 0.009549 rpm | Very slow |
| 0.01 rad/s | 0.09549 rpm | Slow mechanism |
| 0.1 rad/s | 0.9549 rpm | 0.955 rpm |
| 1 rad/s | 9.549 rpm | 9.55 rpm |
| 3.142 rad/s | 30 rpm | π rad/s = 30 rpm |
| 6.283 rad/s | 60 rpm | 1 rps = 60 rpm |
| 10 rad/s | 95.49 rpm | 95.5 rpm |
| 52.36 rad/s | 500 rpm | 500 rpm |
| 100 rad/s | 954.9 rpm | 955 rpm |
| 314.2 rad/s | 3000 rpm | 3,000 rpm motor |
| 628.3 rad/s | 6000 rpm | 6,000 rpm |
| 1000 rad/s | 9549 rpm | 9,549 rpm |
| 1e+04 rad/s | 9.549e+04 rpm | 95,490 rpm |
| 1e+06 rad/s | 9.549e+06 rpm | Very high speed |
rad/s × 9.549 = rpm.
2π rad/s = 60 rpm = 1 rps. 314.2 rad/s = 3,000 rpm.
rpm × π/30 = 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 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 rad/s = 9.549 rpm. Reverse: 1 rpm = 0.1047 rad/s.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.