What this converter does
This converter turns rotational speed between radians per second, revolutions per minute, revolutions per second, hertz and degrees per second — instantly and with exact factors. Type a value, pick the units, and the answer updates as you type.
One revolution is 2π radians, so 1 rad/s equals 60 ÷ 2π ≈ 9.549 rpm. Angular velocity pairs with torque to give power — see the HP to kW converter for the power side.
The units it covers
Every unit measures rotational speed, so each converts through the radian per second with a fixed ratio.
View all units & their values
| Unit | Symbol | Value | Mainly used |
|---|---|---|---|
| Radian per second | rad/s | 1 | SI angular velocity — dynamics |
| Revolutions per minute | rpm | 0.10472 | Motors, engines, machinery |
| Revolutions per second | rps | 6.2832 | High-speed rotation |
| Hertz | Hz | 6.2832 | Rotational frequency (rev/s) |
| Degree per second | °/s | 0.017453 | Gimbals, servos, slow motion |
The formula
Each unit has a fixed value in rad/s, so any conversion goes through the rad/s once:
result = value × factor_from ÷ factor_toWhere:
- value = the number you typed, in the “from” unit
- factor_from = the “from” unit’s value in rad/s
- factor_to = the “to” unit’s value in rad/s
Worked example
Convert 314.16 rad/s to revolutions per minute.
1 rpm = 0.10471975512 rad/s314.16 ÷ 0.10472 = 3000 rpmSo 314.16 rad/s is 3000 rpm — a common motor speed.
The units in this example
The SI unit of angular velocity, used in dynamics and control. One full turn per second is 2π rad/s.
- 1 rad/s ≈ 9.549 rpm
- 1 rad/s ≈ 0.1592 rps
- 2π rad/s = 1 Hz
- 1 rad/s ≈ 57.30 °/s
Turns per minute — the everyday measure of engine, motor and machine speed. One rpm is 2π radians over 60 seconds.
- 1 rpm ≈ 0.10472 rad/s
- 1 rpm = 1/60 rps
- 1 rpm ≈ 0.01667 Hz
- 60 rpm = 1 Hz