What this calculator does
RPM, revolutions per minute, is the everyday unit for how fast something spins: an engine idling, a fan blade, a washing machine drum or a motor shaft. Physics and engineering formulas, however, usually work in hertz (cycles per second) or radians per second (angular velocity), so a value quoted in RPM often needs converting before it can be plugged into another calculation.
This calculator takes one RPM figure and converts it straight to hertz, radians per second and degrees per second, along with revolutions per second and per hour. It is a pure unit conversion: it does not touch gear ratios, wheel diameters or torque, so it works the same way regardless of what is actually spinning.
The formula
One revolution is one full turn, and a minute is 60 seconds, so dividing RPM by 60 gives revolutions per second, which is the same thing as hertz. Each revolution also sweeps through 2π radians (360 degrees), so multiplying the frequency in hertz by 2π gives the angular velocity in radians per second, and by 360 gives degrees per second.
| Term | Meaning |
|---|---|
| RPM | Revolutions per minute: the number of full turns completed in one minute. |
| Hz (hertz) | Cycles per second. For rotation, one hertz equals one revolution per second. |
| rad/s | Radians per second, the standard unit of angular velocity used in physics and engineering formulas. |
The inputs explained
| Field | What to enter |
|---|---|
| Rotational speed (RPM) | The rotational speed you want to convert, in revolutions per minute. |
When to use it
Feeding a physics formula
Formulas for centripetal force, angular momentum or rotational kinetic energy are written in terms of angular velocity in radians per second, not RPM, so a spec sheet quoted in RPM needs converting first.
Comparing a motor spec to a datasheet
Some motor and fan datasheets quote maximum speed in hertz rather than RPM, particularly for AC motors tied to mains frequency. Converting both figures to the same unit makes them directly comparable.
Sanity-checking a sensor reading
A tachometer or encoder may report frequency or angular velocity rather than RPM. Converting back to RPM gives a more intuitive number for a quick sanity check against the expected spin rate.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What do common RPM values convert to?
A spread of everyday rotational speeds, from a slow ceiling fan to a car engine at highway revs.
| RPM | Frequency | Angular velocity (rad/s) |
|---|---|---|
| 60 | 1.000 Hz | 6.283 rad/s |
| 300 | 5.000 Hz | 31.416 rad/s |
| 1,200 | 20.000 Hz | 125.664 rad/s |
| 3,000 | 50.000 Hz | 314.159 rad/s |
| 6,000 | 100.000 Hz | 628.319 rad/s |
Questions
How do I convert RPM to Hz?
Divide by 60. RPM counts revolutions per minute and hertz counts cycles per second, and there are 60 seconds in a minute, so RPM ÷ 60 = Hz.
How do I convert RPM to radians per second?
Multiply RPM by 2π, then divide by 60 (equivalently, multiply the frequency in hertz by 2π). Each revolution is 2π radians, so this converts revolutions per minute into radians per minute, then into radians per second.
Does this calculator account for gear ratios or wheel size?
No, this is a straightforward unit conversion of a single rotational speed. Working out the RPM of one shaft from another via a gear ratio, or a linear speed from a wheel's RPM and diameter, needs those extra figures as separate inputs.
Why do some formulas use rad/s instead of RPM or Hz?
Many rotational physics formulas, such as those for angular momentum or centripetal acceleration, are derived directly in terms of angle swept per second, which is what radians per second measures. Using RPM or Hz in those formulas would need an extra conversion factor built in.
To work out torque from RPM and power, see the motor torque calculator. For torque and RPM combined into other quantities, see the torque calculator.