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Multiple conversions
To convert from revolution per minute (rpm) to millihertz (mHz), use the following formula:
millihertz (mHz)
= 160 × 1000× revolution per minute (rpm)
= 16.666666666666666667× revolution per minute (rpm)
To convert from revolution per minute (rpm) to hertz (Hz), use the following formula:
hertz (Hz)
= 160× revolution per minute (rpm)
= 0.016666666666666666667× revolution per minute (rpm)
To convert from revolution per minute (rpm) to kilohertz (kHz), use the following formula:
kilohertz (kHz)
= 160 × 11000× revolution per minute (rpm)
= 0.000016666666666666666667× revolution per minute (rpm)
To convert from revolution per minute (rpm) to megahertz (MHz), use the following formula:
megahertz (MHz)
= 160 × 1106× revolution per minute (rpm)
= 1.6666666666666666667× 10-8× revolution per minute (rpm)
To convert from revolution per minute (rpm) to gigahertz (GHz), use the following formula:
gigahertz (GHz)
= 160 × 1109× revolution per minute (rpm)
= 1.6666666666666666667× 10-11× revolution per minute (rpm)
To convert from revolution per minute (rpm) to terahertz (THz), use the following formula:
terahertz (THz)
= 160 × 11012× revolution per minute (rpm)
= 1.6666666666666666667× 10-14× revolution per minute (rpm)
To convert from revolution per minute (rpm) to degree per second (deg/s), use the following formula:
degree per second (deg/s)
= 160 × 360× revolution per minute (rpm)
= 6× revolution per minute (rpm)
To convert a rotational speed from revolutions per minute (rpm) to radians per second (rad/s), multiply the value by π ÷ 30 ≈ 0.1047198.
One revolution is 2π radians and one minute is 60 seconds, so the factor is 2π ÷ 60 = π/30. It is the exact reciprocal of the 30/π used in the opposite direction, and like that factor it is irrational: 0.1047198 is a rounding.
A four-pole induction motor on a 50 Hz supply runs at 1,450 rpm under load, and a control model needs the speed in rad/s:
Working in the other direction, multiply by 30 ÷ π ≈ 9.549297: 100 rad/s is 954.93 rpm.
| rpm | rad/s |
|---|---|
| 1 | 0.10472 |
| 100 | 10.472 |
| 500 | 52.360 |
| 1,000 | 104.72 |
| 1,500 | 157.08 |
| 1,800 | 188.50 |
| 3,000 | 314.16 |
| 3,600 | 376.99 |
Motor nameplates, variable-frequency drive parameters and gearbox catalogues are written in rpm, and the round numbers are no accident: a two-pole motor on a 50 Hz supply has a synchronous speed of 3,000 rpm, a four-pole motor 1,500 rpm, and the 60 Hz equivalents are 3,600 and 1,800 rpm. Every one of those becomes an awkward decimal in rad/s, which is exactly why the conversion is needed the moment a nameplate figure enters a dynamics calculation.
Simply put, revolutions per minute (RPM) measures the speed at which something is spinning.
It counts the number of full turns an object completes in one minute. From car engines to computer hard drives, RPM is a key indicator of performance and speed.
The concept of RPM (revolutions per minute) gained popularity during the Industrial Revolution, thanks in large part to Scottish engineer James Watt.
While developing his steam engine, Watt needed a way to compare its power output to that of a horse. To do this, he determined how many times a horse could turn a mill wheel in one minute.
He utilized this rotational measurement to help establish the definition of horsepower. As a result, RPM became a crucial metric for quantifying the performance and work capacity of mechanical engines—a practice that continues to this day.
You encounter RPM every day in common technology.
In your car, the tachometer displays the engine's speed in revolutions per minute, indicating how fast the crankshaft is spinning. A higher RPM generally means more power is being produced.
Computer hard disk drives (HDDs) also use RPM to measure their performance; a 7200 RPM drive can read and write data faster than a 5400 RPM drive.
RPM ratings, which denote motor speed and efficiency, are also found on household appliances such as blenders, washing machines, and fans.
Although RPM is a common unit, physics and engineering often use hertz (Hz) for frequency and radians per second (rad/s) for angular velocity.
The conversion is straightforward:
To Hertz (Hz): Because a minute has 60 seconds, you divide the RPM value by 60.
To Radians per Second (rad/s): One complete rotation is equivalent to 2π radians. To convert RPM to radians per second, multiply the RPM value by 2π, then divide by 60.