About this converter
Angular velocity measures how fast an object rotates around an axis. Radian per second (rad/s) is the SI-compatible reference unit, and 1 revolution per minute equals 0.104719755 rad/s because one full revolution is 2π radians.
This converter supports radians, degrees, and revolutions across seconds, minutes, hours, and days. Mechanical engineers, motor technicians, robotics programmers, astronomers, and physics students use angular velocity conversions for shafts, wheels, turntables, robot joints, and rotating celestial objects.
How to Use This Converter
- Enter the angular velocity value.
- Select the source unit from the From menu.
- Select the target unit from the To menu.
- Read the converted result and formula line.
- Use Swap to reverse the selected units.
Units Covered
| Unit | Symbol | Common Use |
|---|---|---|
| Radian/second | rad/s | Physics equations, control systems, and rotational dynamics. |
| Radian/minute | rad/min | Slow rotation rates expressed with radian measure. |
| Radian/hour | rad/h | Long-duration rotation and astronomy-style calculations. |
| Radian/day | rad/d | Very slow rotation rates over daily periods. |
| Degree/second | deg/s | Servos, tracking systems, and angular motion in degrees. |
| Degree/minute | deg/min | Slow angular drift, navigation, and instrument readings. |
| Degree/hour | deg/h | Astronomy, rotation drift, and long-duration pointing systems. |
| Degree/day | deg/d | Celestial motion and slow orientation changes. |
| Revolution/second | rev/s | Fast rotating shafts, wheels, and test rigs. |
| Revolution/minute | RPM | Motors, engines, fans, drills, and rotating machinery. |
| Revolution/hour | rev/h | Slow industrial equipment and low-speed mechanisms. |
| Revolution/day | rev/d | Very slow rotators, timers, and astronomy references. |
RPM to rad/s Conversion Table
| From | To |
|---|---|
| 1 RPM | 0.10472 rad/s |
| 10 RPM | 1.0472 rad/s |
| 30 RPM | 3.14159 rad/s |
| 60 RPM | 6.28319 rad/s |
| 100 RPM | 10.472 rad/s |
| 250 RPM | 26.1799 rad/s |
| 500 RPM | 52.3599 rad/s |
| 1,000 RPM | 104.72 rad/s |
| 1,500 RPM | 157.08 rad/s |
| 3,000 RPM | 314.159 rad/s |
| 6,000 RPM | 628.319 rad/s |
| 10,000 RPM | 1,047.2 rad/s |
How to Convert RPM to rad/s
RPM to radians per second
For example, 1,800 RPM x 6.283185 / 60 = 188.496 rad/s.
Radians per second to RPM
For example, 100 rad/s x 60 / 6.283185 = 954.93 RPM.
When You Need to Convert Angular Velocity
Motor datasheets usually list shaft speed in RPM, while dynamics equations use rad/s. A motor running at 3,600 RPM equals 376.991 rad/s, which can be used directly in power and torque calculations.
Robotics systems often mix units: a joint controller may command degrees per second, while a simulation model expects radians per second. A joint moving at 90 deg/s equals 1.5708 rad/s.
Astronomy and tracking systems use slower angular rates such as degrees per hour or degrees per day. Converting those values to rad/s helps engineers feed the same rotation rate into control software and physics models.