Radians Per Second to Rpm
Convert radians per second to rpm instantly — one radian per second is 9.5493 rpm.
| Radians Per Second | Rpm |
|---|---|
| 1 rad/s | 9.549297 rpm |
| 2 rad/s | 19.098593 rpm |
| 3 rad/s | 28.64789 rpm |
| 5 rad/s | 47.746483 rpm |
| 10 rad/s | 95.492966 rpm |
| 25 rad/s | 238.732415 rpm |
| 50 rad/s | 477.464829 rpm |
| 100 rad/s | 954.929659 rpm |
How to use
- Enter a value in the Radians Per Second field.
- The Rpm figure appears immediately — no button to press.
- Typing in the Rpm field converts back to Radians Per Second the same way.
- Use the reference table for the values that come up most often.
Radians Per Second to Rpm formula
To convert radians per second to rpm, multiply by 9.54929659.
rpm = rad/s × 9.54929659
Why this factor: the radian per second and the revolution per minute are both defined against the hertz, so dividing one definition by the other gives 9.54929659 directly. Both definitions are set out in full below.
To go the other way, divide by 9.54929659 — or use the Rpm to Radians Per Second converter, which is the same calculation reversed.
Worked example
Start with 60 rad/s. Multiply by 9.54929659 to get 572.957795 rpm.
60 rad/s × 9.54929659 = 572.957795 rpm
The converter above does this for any value you type, in either direction.
What is a radian per second?
Radians per second is the SI measure of angular velocity — how fast an angle is swept out.
Definition: One full revolution is 2π radians, so 1 rad/s equals 1/(2π) hertz, about 0.159155 Hz.
Where it is used: Rotational dynamics, control systems, signal processing, and motor modeling.
Worth knowing: Angular velocity and frequency are related but not identical quantities; the 2π factor is exactly what separates them.
What is a revolution per minute?
Revolutions per minute measures rotational speed as complete turns each minute.
Definition: One revolution per minute is exactly 1/60 hertz.
Where it is used: Engine and motor speeds, hard drive and fan speeds, and centrifuge settings.
Radians Per Second vs Rpm
The radian per second is an SI unit while the revolution per minute is a specialized unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many rpm are in a radian per second?
One radian per second equals 9.54929659 rpm.
What is the formula to convert radians per second to rpm?
Multiply the number of radians per second by 9.54929659. To reverse it, divide by 9.54929659 instead.
How do I convert rpm back to radians per second?
Divide by 9.54929659, which is the same as multiplying by 0.104719755.
How many rpm are in 10 radians per second?
10 rad/s works out to 95.492966 rpm.
Is there anything to watch out for with radians per second?
Angular velocity and frequency are related but not identical quantities; the 2π factor is exactly what separates them.
How is the radian per second defined?
One full revolution is 2π radians, so 1 rad/s equals 1/(2π) hertz, about 0.159155 Hz.