Hertz to RPM Converter
Free Hertz rpmconverter Converter for signal & frequency units. Enter a value to see equivalent measurements across systems.
Hertz to RPM Converter
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Formula: RPM = Hertz * 60 | Hertz = RPM / 60
Worked example โ 50 Hz 4-pole motor: 1,500 RPM synchronous speed
Formula
RPM = Hertz * 60 | Hertz = RPM / 60
Multiply hertz by 60 to get RPM since there are 60 seconds per minute. For motor synchronous speed, use RPM = (120 * f) / poles. Angular velocity in rad/s equals 2 * pi * frequency in Hz.
Worked Examples
Example 1: European Power Motor Speed
Problem:A 4-pole motor operates on 50 Hz European power. What is its synchronous speed?
Solution:Rotational frequency: 50 Hz = 50 * 60 = 3,000 RPM Synchronous speed = (120 * 50) / 4 = 1,500 RPM Angular velocity = 2 * pi * 50 = 314.16 rad/s
Result:50 Hz 4-pole motor: 1,500 RPM synchronous speed
Example 2: Hard Drive Spindle Speed
Problem:A hard drive spins at 7,200 RPM. What is the frequency in hertz?
Solution:Frequency = RPM / 60 f = 7,200 / 60 = 120 Hz Period = 1 / 120 = 0.00833 seconds Angular velocity = 2 * pi * 120 = 753.98 rad/s
Result:7,200 RPM = 120 Hz (period of 8.33 ms per revolution)
Frequently Asked Questions
How do you convert hertz to RPM?
To convert hertz to RPM (revolutions per minute), multiply the frequency in hertz by 60. This works because hertz measures cycles per second and there are 60 seconds in a minute. For example, 50 Hz equals 50 * 60 = 3,000 RPM. Conversely, to convert RPM to hertz, divide the RPM value by 60. A motor spinning at 1,800 RPM has a rotational frequency of 1,800 / 60 = 30 Hz.
What is synchronous motor speed and how does it relate to frequency?
Synchronous motor speed is determined by the power supply frequency and the number of magnetic poles in the motor. The formula is RPM = (120 * f) / P, where f is frequency in hertz and P is the number of poles. A 2-pole motor on 60 Hz power runs at 3,600 RPM synchronously, while a 4-pole motor on the same supply runs at 1,800 RPM. Actual induction motors run slightly slower due to slip.
What is angular velocity and how is it calculated?
Angular velocity (omega) measures rotational speed in radians per second. It is calculated as omega = 2 * pi * f, where f is the frequency in hertz. One complete revolution equals 2*pi radians (approximately 6.2832 radians). Angular velocity is preferred in physics and engineering equations because it simplifies the mathematics of rotational motion, torque, and centripetal force calculations.
Why are 50 Hz and 60 Hz the standard power frequencies worldwide?
The 50 Hz and 60 Hz standards evolved historically from early electrical system development. The United States standardized on 60 Hz largely due to the influence of Westinghouse and Tesla, while Europe adopted 50 Hz following German engineering preferences. Higher frequencies allow lighter transformers but increase transmission losses, while lower frequencies are better for long-distance transmission. Both frequencies represent practical compromises between equipment size, efficiency, and flicker-free lighting.
What is the rotational period and how do I find it from frequency?
The period is the time for one complete revolution and is the reciprocal of frequency, T = 1 / f. A shaft turning at 3,000 RPM has a frequency of 3,000 / 60 = 50 Hz, so its period is 1 / 50 = 0.02 seconds, or 20 milliseconds per revolution. Period is what you actually measure on an oscilloscope or with a stroboscope, and it is the natural input for timing work such as ignition advance, encoder pulse spacing and vibration sampling intervals.
What is motor slip and how much does it reduce actual RPM?
An induction motor must run slower than synchronous speed so its rotor cuts flux lines and produces torque. Slip is that shortfall as a fraction, s = (Ns - N) / Ns, where Ns is synchronous speed. Full-load slip in general-purpose induction motors is typically a few percent. A four-pole motor on 60 Hz has Ns = 1,800 RPM, so 3 percent slip gives 1,800 x 0.97 = 1,746 RPM under load. Slip approaches zero at no load and rises as the mechanical load increases.
How do I find the number of poles from a nameplate RPM?
Rearrange the synchronous speed relation to P = (120 x f) / Ns. Nameplate speeds are full-load speeds and already include slip, so round up to the nearest synchronous value first. A motor stamped 1,750 RPM on a 60 Hz supply is clearly a nominal 1,800 RPM machine, giving P = (120 x 60) / 1,800 = 4 poles. That same motor on a 50 Hz supply would synchronise at (120 x 50) / 4 = 1,500 RPM, which is why imported machines run about 17 percent slower on the other standard.
How do I convert RPM into surface speed at a given radius?
Convert to angular velocity first, then multiply by radius: v = omega x r, where omega = 2 x pi x f in radians per second. A wheel turning at 300 RPM is 5 Hz, so omega = 2 x pi x 5 = 31.42 rad/s, and at a radius of 0.3 m the rim speed is 31.42 x 0.3 = 9.42 m/s. This is the calculation behind cutting speed on a lathe, belt speed over a pulley and tip speed on a fan, all of which are limited by material strength rather than by RPM alone.
Why do variable frequency drives change speed by changing hertz?
Synchronous speed is set entirely by supply frequency and pole count, and pole count is fixed by the winding, so frequency is the only variable left. A VFD rectifies the incoming AC and synthesises a new waveform at the commanded frequency. It must also scale voltage in proportion, holding the volts-per-hertz ratio roughly constant, because otherwise the magnetic flux in the core rises as frequency falls and the motor saturates and overheats. At very low frequencies extra voltage boost compensates for winding resistance.
Is a hertz the same thing as a revolution per second?
Dimensionally yes, since both reduce to reciprocal seconds, and numerically one revolution per second equals one hertz. The distinction is in meaning: hertz counts cycles of any periodic event, while revolutions per second counts whole turns of a physical shaft. The gap opens once angular velocity in radians per second enters, because one revolution is 2 x pi radians, so 1 Hz corresponds to 6.2832 rad/s. Mixing radians per second with revolutions per second introduces a stray factor of about 6.28.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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