Rpm to Radians Per Second
Convert rpm to radians per second instantly — one revolution per minute is 0.10472 radians per second.
| Rpm | Radians Per Second |
|---|---|
| 1 rpm | 0.10472 rad/s |
| 2 rpm | 0.20944 rad/s |
| 3 rpm | 0.314159 rad/s |
| 5 rpm | 0.523599 rad/s |
| 10 rpm | 1.047198 rad/s |
| 25 rpm | 2.617994 rad/s |
| 50 rpm | 5.235988 rad/s |
| 100 rpm | 10.471976 rad/s |
How to use
- Enter a value in the Rpm field.
- The Radians Per Second figure appears immediately — no button to press.
- Typing in the Radians Per Second field converts back to Rpm the same way.
- Use the reference table for the values that come up most often.
Rpm to Radians Per Second formula
To convert rpm to radians per second, multiply by 0.104719755.
rad/s = rpm × 0.104719755
Why this factor: the revolution per minute and the radian per second are both defined against the hertz, so dividing one definition by the other gives 0.104719755 directly. Both definitions are set out in full below.
To go the other way, divide by 0.104719755 — or use the Radians Per Second to Rpm converter, which is the same calculation reversed.
Worked example
Take 50 rpm and multiply by the factor 0.104719755: the result is 5.235988 rad/s.
50 rpm × 0.104719755 = 5.235988 rad/s
The converter above does this for any value you type, in either direction.
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.
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.
Rpm vs Radians Per Second
The revolution per minute is a specialized unit while the radian per second is an SI 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 radians per second are in a revolution per minute?
One revolution per minute equals 0.104719755 radians per second.
What is the formula to convert rpm to radians per second?
Multiply the number of rpm by 0.104719755. To reverse it, divide by 0.104719755 instead.
How do I convert radians per second back to rpm?
Divide by 0.104719755, which is the same as multiplying by 9.54929659.
How many radians per second are in 10 rpm?
10 rpm works out to 1.047198 rad/s.
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 revolution per minute defined?
One revolution per minute is exactly 1/60 hertz.