Convert angular velocity units — rad/s, deg/s, RPM, RPS and more.
| Unit | Name | Value |
|---|---|---|
| rad/s | Radian/Second | 0.016667 |
| °/s | Degree/Second | 0.95494835 |
| rpm | Revolution/Minute | 0.15915775 |
| rps | Revolution/Second | 0.0026526377 |
Formula: Degree/Second = Radian/Second × 57.3
Multiply any Radian/Second value by 57.3 to get Degree/Second.
Reverse: Radian/Second = Degree/Second × 0.01745
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rad/s = 57.3 °/s
| Radian/Second (rad/s) | Degree/Second (°/s) | Context |
|---|---|---|
| 7.270e-05 rad/s | 0.004165 °/s | Earth rotation |
| 0.001 rad/s | 0.0573 °/s | Very slow |
| 0.01 rad/s | 0.573 °/s | Slow mechanism |
| 0.1 rad/s | 5.73 °/s | 0.955 rpm |
| 1 rad/s | 57.3 °/s | 9.55 rpm |
| 3.142 rad/s | 180 °/s | π rad/s = 30 rpm |
| 6.283 rad/s | 360 °/s | 1 rps = 60 rpm |
| 10 rad/s | 573 °/s | 95.5 rpm |
| 52.36 rad/s | 3000 °/s | 500 rpm |
| 100 rad/s | 5730 °/s | 955 rpm |
| 314.2 rad/s | 1.8e+04 °/s | 3,000 rpm motor |
| 628.3 rad/s | 3.6e+04 °/s | 6,000 rpm |
| 1000 rad/s | 5.73e+04 °/s | 9,549 rpm |
| 1e+04 rad/s | 5.73e+05 °/s | 95,490 rpm |
| 1e+06 rad/s | 5.73e+07 °/s | Very high speed |
rad/s × 180/π = °/s. Round to × 57.3.
π rad/s = 180°/s. 2π rad/s = 360°/s = 1 rps.
°/s × π/180 = 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.
Degree per second (°/s) measures angular velocity in degrees per unit time. One full revolution = 360°/s, so 1°/s = π/180 rad/s ≈ 0.01745 rad/s. It is widely used in navigation, robotics, and human motion analysis where degree values are more intuitive.
°/s is used in gyroscope specifications, aircraft attitude rates, and game controller sensitivity. MEMS gyroscopes in smartphones typically measure ±250 to ±2,000 °/s. Aircraft maximum roll rate is typically 30–200 °/s. Robotic joint speeds are often specified in °/s.
Interesting fact: Fighter pilots experience angular accelerations up to 400°/s² during high-g maneuvers. The human vestibular system can detect angular velocities as low as 0.5°/s and accelerations as low as 0.1°/s² — making it a remarkably sensitive gyroscope.
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 = 57.3 °/s. Reverse: 1 °/s = 0.01745 rad/s.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.