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: Radian/Minute = Degree/Second × 1.047
Multiply any Degree/Second value by 1.047 to get Radian/Minute.
Reverse: Degree/Second = Radian/Minute × 0.9549
Key chain: 60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s
Common angular speeds — factor: 1 °/s = 1.047 rad/min
| Degree/Second (°/s) | Radian/Minute (rad/min) | Context |
|---|---|---|
| 0.0042 °/s | 0.004398 rad/min | Earth rotation |
| 0.01 °/s | 0.01047 rad/min | Very slow |
| 0.1 °/s | 0.1047 rad/min | 0.017 rpm |
| 1 °/s | 1.047 rad/min | 0.167 rpm |
| 6 °/s | 6.283 rad/min | 1 rpm |
| 57.3 °/s | 60 rad/min | ~10 rpm |
| 180 °/s | 188.5 rad/min | 30 rpm |
| 360 °/s | 377 rad/min | 1 rps = 60 rpm |
| 1800 °/s | 1885 rad/min | 300 rpm |
| 3600 °/s | 3770 rad/min | 600 rpm |
| 1.8e+04 °/s | 1.885e+04 rad/min | 3,000 rpm |
| 3.6e+04 °/s | 3.77e+04 rad/min | 6,000 rpm |
| 1e+05 °/s | 1.047e+05 rad/min | 16,667 rpm |
| 1e+06 °/s | 1.047e+06 rad/min | Very fast |
| 1.000e+09 °/s | 1.047e+09 rad/min | Extreme |
1 °/s = 1.047 rad/min.
60 rpm = 1 rps = 2π rad/s ≈ 6.283 rad/s = 360°/s. Memorize this chain.
Multiply result by 0.9549 to recover the original °/s value.
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.
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.
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 °/s = 1.047 rad/min. Reverse: 1 rad/min = 0.9549 °/s.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.