RPM to Angular Velocity
Convert revolutions per minute into angular velocity in radians per second for motors, shafts, and physics work.
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RPM to Angular Velocity Table
| Revolutions per Minute | Angular Velocity |
|---|---|
| 1 | 0.10471976 |
| 10 | 1.04719755 |
| 30 | 3.14159265 |
| 60 | 6.28318531 |
| 120 | 12.56637061 |
| 300 | 31.41592654 |
| 600 | 62.83185307 |
| 900 | 94.24777961 |
| 1,200 | 125.66370614 |
| 1,800 | 188.49555922 |
| 2,400 | 251.32741229 |
| 3,600 | 376.99111843 |
Popular Conversions
- 30 revolutions per minute = 3.14159265 angular velocity
- 60 revolutions per minute = 6.28318531 angular velocity
- 120 revolutions per minute = 12.56637061 angular velocity
- 300 revolutions per minute = 31.41592654 angular velocity
- 600 revolutions per minute = 62.83185307 angular velocity
- 900 revolutions per minute = 94.24777961 angular velocity
- 1,200 revolutions per minute = 125.66370614 angular velocity
- 1,800 revolutions per minute = 188.49555922 angular velocity
What is Revolutions per Minute and Radian per Second?
Revolutions per Minute
Definition: Revolutions per minute show how many full turns happen in one minute.
History/origin: RPM became common with engines, motors, gears, and mechanical equipment.
Current use: RPM is used for vehicles, fans, tools, records, and rotating machinery.
Radian per Second
Definition: Radians per second measure angular speed using radians over time.
History/origin: Angular-speed units became important in mechanics, wave motion, and rotating systems.
Current use: Radians per second are used in physics, motors, turbines, and control systems.
Related Time Unit Conversions
Angular velocity is closely linked with RPM, hertz, rad/s, and other rotation measures.
| From RPM To | Conversion Factor | Formula |
|---|---|---|
| RPS | ÷ 60 | RPS = RPM ÷ 60 |
| Hertz | ÷ 60 | Hz = RPM ÷ 60 |
| rad/s | × 2π ÷ 60 | rad/s = RPM × 2π ÷ 60 |
| Angular Velocity | × 2π ÷ 60 | Angular Velocity = RPM × 2π ÷ 60 |
| Period | 60 ÷ RPM | Period = 60 ÷ RPM |
| Degrees per Second | × 6 | deg/s = RPM × 6 |
| Cycles per Minute | same value | RPM is already cycles per minute |
| Wheel speed to MPH | needs diameter | MPH requires RPM plus wheel circumference |
Typical Use Cases
Frequently Asked Questions
Q: Why does RPM to radians per second use 2pi?
A: One full revolution equals 2pi radians. The converter first changes revolutions per minute into revolutions per second, then multiplies by 2pi to express the same spin rate as angular travel each second.
Q: What is a good checkpoint for RPM to Angular Velocity?
A: 60 revolutions per minute becomes 6.28318531 angular velocity, which is a clean reference when checking motor speed against a physics or controls formula.
Q: What does angular velocity mean in plain language?
A: Angular velocity tells you how quickly an object sweeps through angle, rather than how many turns it makes in a minute. Engineers often want rad/s because many formulas are written in angular units.
Q: Why not stay in RPM for every calculation?
A: RPM is convenient for dashboards and motor labels, but equations for torque, inertia, and rotational dynamics are usually written with angular velocity in radians per second.
Q: How do I convert Angular Velocity back into RPM?
A: RPM = Angular Velocity × 60 ÷ 2π. That reverse step divides by 2pi and scales back to minutes.
Q: Is this conversion approximate?
A: The relationship itself is exact. Only the displayed decimal output may be rounded for readability.