Frequency Converter
Convert a frequency between Hz, kHz, MHz, GHz, THz, rpm, rad/s, and deg/s. Enter a Frequency value, then choose the From unit and To unit.
Convert Frequency Between Units
Frequency Conversion Formula
Where:
- \(f_{\mathrm{from}}\) — the entered Frequency value in the selected From unit
- \(f_{\mathrm{to}}\) — the Converted Frequency Value in the selected To unit
- \(C_{\mathrm{from}}\) and \(C_{\mathrm{to}}\) — the number of hertz represented by one unit of each selected type
The calculator first converts the input to hertz, then divides by the hertz-per-unit factor for the target unit. For rotational units, one full revolution is treated as one cycle.
Frequency – Calculation Example
Example: using the default settings, convert a frequency of 60 hertz to kilohertz.
One kilohertz equals 1,000 hertz, so \(C_{\mathrm{from}}=1\) and \(C_{\mathrm{to}}=1{,}000\).
\[ 60\,\mathrm{Hz}\times\frac{1\,\mathrm{Hz/Hz}}{1{,}000\,\mathrm{Hz/kHz}}=0.06\,\mathrm{kHz} \]
Result: 60 Hz = 0.06 kHz.
How to use the calculator
- Enter a nonnegative number in Frequency value. The default is 60.
- Choose the input unit in From unit. The default is Hertz (Hz).
- Choose the unit you want in To unit. The default is Kilohertz (kHz).
- Read Converted Frequency Value. The result includes the target unit.
To reverse a conversion, swap the From unit and To unit selections and enter the converted number as the new Frequency value. Selecting the same unit in both fields leaves the value unchanged.
What frequency and rotational rate mean
Frequency counts how many complete cycles occur per second. One hertz (Hz) means one cycle per second; hertz is the SI derived unit of frequency. The metric prefixes scale this rate: a kilohertz is 1,000 Hz, a megahertz is one million Hz, a gigahertz is one billion Hz, and a terahertz is one trillion Hz. These units make very small or large cycle rates easier to read without changing the underlying quantity.
Revolutions per minute (rpm) describes complete turns in one minute. Radians per second (rad/s) and degrees per second (deg/s) describe how quickly an angle changes. The calculator relates all three to hertz by treating each complete turn—\(2\pi\) radians or 360 degrees—as one cycle. For example, 60 rpm is one revolution per second, or 1 Hz; that same rotation rate is \(2\pi\) rad/s or 360 deg/s.
This distinction matters when interpreting a result. A motor turning at 60 rpm has a rotation rate of 1 Hz, but a measurement associated with that motor could repeat more than once per turn. If a sensor produces four pulses per revolution, it produces four pulses per second at 60 rpm. Convert the rotational rate here, then account separately for the number of events per turn.
Frequency also appears in electrical signals, sound, and mechanical vibration. A 60 Hz alternating-current waveform completes 60 cycles each second; that does not mean an attached motor necessarily turns at 60 revolutions per second. When comparing quantities, first check what constitutes one cycle. For related measurements in other units, see the Electric Current converter, Sound converter, or Torque converter.
Conversion factors and practical limits
The calculator uses hertz as an intermediate unit. The table shows how many hertz correspond to one unit of each supported type:
| Unit | Equivalent in hertz |
|---|---|
| Hz | 1 Hz |
| kHz | 1,000 Hz |
| MHz | 1,000,000 Hz |
| GHz | 1,000,000,000 Hz |
| THz | 1,000,000,000,000 Hz |
| rpm | 1/60 Hz |
| rad/s | \(1/(2\pi)\) Hz |
| deg/s | 1/360 Hz |
These are unit conversions, not predictions about a physical system. The rad/s conversion assumes the angle describes a repeating rotation, with one complete cycle per \(2\pi\) radians. For oscillations, angular frequency is often written \(\omega=2\pi f\); do not confuse its numerical value in rad/s with the frequency in Hz.
The input does not accept negative values, and the displayed result is rounded to at most 10 decimal places. A very small nonzero result may therefore display as zero in a larger target unit. If that happens, choose a smaller unit, such as Hz instead of GHz, to see a more useful number. A frequency of zero can be converted between units, but it has no finite period: the relationship \(T=1/f\) applies only when \(f>0\).
Frequently Asked Questions
How do I convert rpm to rad/s by hand?
Multiply rpm by \(2\pi/60\). For example, 1,200 rpm is 20 revolutions per second, so its angular speed is \(20\times2\pi=40\pi\), or approximately 125.66 rad/s. To convert back, multiply rad/s by \(60/(2\pi)\). This assumes one full revolution corresponds to one cycle.
What is a normal frequency?
There is no single normal frequency; it depends on what is cycling. Mains electricity is typically 50 or 60 Hz, while the commonly cited range of human hearing is roughly 20 Hz to 20 kHz. A motor, radio signal, or vibration may have a very different expected range. Compare a result with the specifications for the particular system, not with a universal target.
How do I convert a period in milliseconds to frequency?
Convert the period to seconds, then take its reciprocal: \(f=1/T\). A period of 2.5 milliseconds is 0.0025 seconds, giving \(f=400\) Hz. Period and frequency are inversely related, so a shorter period means a higher frequency. This calculation requires a positive, nonzero period.
Why can frequency be negative in a Fourier transform?
A negative Fourier frequency describes a component rotating in the opposite direction in the complex-number representation of a signal; it does not mean a negative count of physical cycles. For a real-valued signal, positive- and negative-frequency components appear as conjugate pairs. Use the nonnegative magnitude when converting a physical cycle rate with this calculator.
Can I convert a light frequency in THz to a wavelength in nanometers?
Yes, but wavelength is not another frequency unit, so it requires a separate calculation. In vacuum, divide the speed of light by frequency: \(\lambda=c/f\). For example, 500 THz corresponds to approximately 600 nm in vacuum. In a material, light travels more slowly and its wavelength changes, although its frequency remains the same.
Why does a motor’s rpm differ from the frequency of its AC supply?
Supply frequency alone does not determine motor speed. An AC motor’s synchronous speed also depends on its number of magnetic poles: \(n=120f/P\) rpm, where \(P\) is the pole count. A four-pole motor on a 60 Hz supply has a synchronous speed of 1,800 rpm. An induction motor typically runs somewhat slower because it needs slip to produce torque.
Why is a conversion involving rad/s not exact on the display?
Conversions between Hz and rad/s involve \(\pi\), whose decimal expansion never ends. For instance, 1 Hz equals exactly \(2\pi\) rad/s, but any displayed decimal is an approximation. The calculator also limits displayed decimal places, so converting a rounded result back may not reproduce every digit of the original value. Keep extra precision during intermediate calculations when accuracy matters.
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