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: Radian/Minute = Radian/Second × 60
Multiply any Radian/Second value by 60 to get Radian/Minute.
Reverse: Radian/Second = Radian/Minute × 0.01667
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 rad/s = 60 rad/min
| Radian/Second (rad/s) | Radian/Minute (rad/min) | Context |
|---|---|---|
| 7.270e-05 rad/s | 0.004362 rad/min | Earth rotation |
| 0.001 rad/s | 0.06 rad/min | Very slow |
| 0.01 rad/s | 0.6 rad/min | Slow mechanism |
| 0.1 rad/s | 6 rad/min | 0.955 rpm |
| 1 rad/s | 60 rad/min | 9.55 rpm |
| 3.142 rad/s | 188.5 rad/min | π rad/s = 30 rpm |
| 6.283 rad/s | 377 rad/min | 1 rps = 60 rpm |
| 10 rad/s | 600 rad/min | 95.5 rpm |
| 52.36 rad/s | 3142 rad/min | 500 rpm |
| 100 rad/s | 6000 rad/min | 955 rpm |
| 314.2 rad/s | 1.885e+04 rad/min | 3,000 rpm motor |
| 628.3 rad/s | 3.77e+04 rad/min | 6,000 rpm |
| 1000 rad/s | 6e+04 rad/min | 9,549 rpm |
| 1e+04 rad/s | 6e+05 rad/min | 95,490 rpm |
| 1e+06 rad/s | 6e+07 rad/min | Very high speed |
rad/s × 60 = rad/min. Exact.
1 rad/s = 60 rad/min.
rad/min ÷ 60 = 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.
Radian per minute (rad/min) equals 1/60 rad/s and is used for slow rotations in industrial processes, telescope tracking, and clock mechanisms where per-second rates would be too small. 60 rad/min = 1 rad/s; 2π rad/min ≈ 1 rpm.
Telescope mounts track celestial objects at about 0.0042 rad/min (compensating for Earth's rotation). Slow industrial mixers and stirrers operate at 1–30 rad/min. Clock minute hands rotate at 2π rad/hr = π/30 rad/min ≈ 0.105 rad/min.
Interesting fact: The minute hand of a clock rotates at exactly π/30 rad/min = 2π rad/hour. The hour hand rotates at π/360 rad/min = 2π rad/12 hours. The second hand at 2π rad/min = 1 rps = 6°/s — the only hand with a speed convenient to express in multiple units.
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 = 60 rad/min. Reverse: 1 rad/min = 0.01667 rad/s.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.