About the Frequency Calculator
Frequency is how often something repeats each second, measured in hertz (Hz). A pendulum swinging once a second has a frequency of 1 Hz; mains electricity alternates 50 or 60 times a second; the note A above middle C vibrates 440 times a second; and visible light oscillates hundreds of trillions of times a second. Frequency is the language of waves, vibrations, rotations and electronic signals.
This frequency calculator finds frequency in four ways: from the period of one cycle, from a wave's speed and wavelength, from an angular frequency in radians per second, or from a rotation speed in revolutions per minute. It always shows the period and angular frequency too, and describes where the frequency sits — in the range of hearing, in the radio spectrum or in visible light.
How to Use the Frequency Calculator
Choose From period, From speed and wavelength, From angular frequency or From rpm.
Enter the value and choose its unit.
For a wave, choose the type of wave — light, sound in air, water or steel — or enter a custom wave speed.
The Formulas
from period f = 1 ÷ T
from speed, wavelength f = v ÷ λ
from angular frequency f = ω ÷ 2π
from rotation speed f = rpm ÷ 60
period T = 1 ÷ f
angular frequency ω = 2πfStep-by-Step Examples
A period of 20 milliseconds.
f = 1 ÷ 0.02 = 50 Hz
ω = 2π × 50 = 314.16 rad/sA motor at 3,000 rpm: f = 3,000 ÷ 60 = 50 Hz.
An angular frequency of 314.159 rad/s: f = 314.159 ÷ 2π = 50 Hz.
A sound wave 0.78 m long in air (343 m/s):
f = 343 ÷ 0.78 = 439.74 HzRed light at 650 nm:
f = 299,792,458 ÷ (650 × 10⁻⁹) = 4.6122 × 10¹⁴ Hz = 461.22 THzFrequency and Period
Frequency and period are two views of the same thing. The period is the time for one complete cycle; the frequency is the number of cycles per second. They are reciprocals: a 50 Hz supply has a period of 20 ms, and a 1 kHz tone a period of 1 ms. Engineers measure the period on an oscilloscope screen, then take its reciprocal to find the frequency. The unit hertz honours Heinrich Hertz, who first demonstrated radio waves in the 1880s.
Angular Frequency
In the mathematics of oscillations and alternating current, frequency is often expressed as an angular frequency, ω, in radians per second. One full cycle is 2π radians, so ω = 2πf. Equations such as x = A sin(ωt) for a vibrating spring, or the impedance of capacitors and inductors in AC circuits, are neater in angular form. Mains electricity at 50 Hz has an angular frequency of about 314 rad/s; at 60 Hz, about 377 rad/s.
Rotational Frequency
Anything that spins has a frequency: engines, fans, hard drives, washing machine drums and turbines. Rotation speed is usually quoted in revolutions per minute, so dividing by 60 gives hertz. A car engine idling at 800 rpm turns about 13.3 times a second; a drill at 3,000 rpm turns 50 times a second. Power station generators in 50 Hz countries turn at speeds chosen so that the electricity they produce is exactly 50 Hz.
Frequencies of Sound
Human hearing spans roughly 20 Hz to 20 kHz in young people, with the upper limit falling with age. Low frequencies sound deep: a bass guitar's lowest string is about 41 Hz. High frequencies sound shrill: the top note of a piano is about 4,186 Hz, and cymbals and birdsong reach far higher harmonics. Each octave doubles the frequency, so A4 at 440 Hz is followed by A5 at 880 Hz. Below 20 Hz is infrasound, felt more than heard; above 20 kHz is ultrasound, used for medical scans and by bats and dolphins.
Frequencies of Electromagnetic Waves
Radio broadcasts use frequencies from kilohertz to hundreds of megahertz; mobile phones and Wi-Fi use gigahertz. Infrared, visible light and ultraviolet lie in the terahertz and petahertz range — visible light spans roughly 400 to 790 THz. Because all electromagnetic waves travel at the speed of light, their frequency and wavelength are tied together: higher frequency always means shorter wavelength and more energy per photon.
Measuring Frequency
Frequency can be measured in many ways. An oscilloscope displays a signal so its period can be read directly. A frequency counter counts cycles over a fixed time. For rotating machinery, a stroboscope flashing at the right rate makes a spinning part appear to stand still, and optical or magnetic tachometers count revolutions. Musicians use electronic tuners, which measure the frequency of a note and compare it with the correct pitch. Even a smartphone microphone and a free app can measure the frequency of a whistle or a guitar string to within a fraction of a hertz.
Understanding Your Result
The headline is the frequency, with a suitable prefix such as kHz, MHz or THz.
The period line gives the time for one cycle.
The angular frequency line gives ω in radians per second and the cycles per minute.
The context line places the frequency in the range of hearing or the spectrum.
When Should You Use This Calculator?
Use it for physics homework on waves and oscillations.
Use it to convert between rpm, hertz and radians per second.
Use it to find the frequency of a sound or light wave from its wavelength.
Common Mistakes
Confusing period and frequency. One is the reciprocal of the other.
Forgetting to divide rpm by 60. Hertz means cycles per second, not per minute.
Mixing up ω and f. Angular frequency is 2π times the frequency.
Using the wrong wave speed. Sound and light travel at very different speeds.