Convert a rotational speed between RPM (revolutions per minute), radians per second, and hertz.
How it works
One revolution is 2π radians, and one hertz is one cycle per second, so rad/s = RPM × 2π ÷ 60 and Hz = RPM ÷ 60. An engine spinning at 3,000 RPM is turning at about 314.16 rad/s, or 50 Hz.
What this does not include
This is distinct from this site’s angular velocity calculator, which computes angular velocity in rad/s from an angle swept over time — this page instead converts an already-known rotational speed between its common units.
How to use this calculator
- Enter the speed in RPM.
A worked example
3,000 RPM converts to angular velocity of 314.1593 rad/s, or a frequency of 50 Hz.
60 RPM converts to 6.2832 rad/s, or 1 Hz — exactly one revolution per second.
What the variables mean
| Variable | Meaning |
|---|---|
| RPM | Revolutions per minute |
| Rad/s | Angular velocity in radians per second |
| Hz | Frequency, in cycles per second |
Edge cases worth knowing
60 RPM always equals exactly 1 Hz — a useful anchor point, since 60 revolutions per minute is by definition one revolution per second.
A missing RPM value makes the conversion impossible, so the calculator declines to show a result without one.
Why do engineers use radians per second instead of RPM in formulas?
Radians are the natural unit for angle in calculus and physics formulas — many rotational-motion equations come out cleaner in rad/s than in RPM, which is more of a practical, everyday unit.
What does hertz measure in a rotational context?
Hertz counts full revolutions per second, making it directly comparable to other frequency measurements like electrical AC frequency (commonly 50 or 60 Hz).
Why is idle engine speed usually quoted in RPM rather than Hz?
RPM is the traditional, intuitive unit in automotive and mechanical contexts — a car idling at “800 RPM” is more immediately meaningful to most people than “13.3 Hz,” even though they describe the same rotational speed.
