Frequency Calculator

This frequency calculator tool is used to calculate the frequency of waves and it works for all directions. You can either input a known period, wave speed, wavelength or frequency itself and then the tool will compute the remaining values and display the frequency as the main result.

Since frequency and period are reciprocals of each other they are computed together by default. The wave speed and wavelength both determine the scale of the wave.

What is frequency?

Frequency is how often a wave repeats itself. It is measured by counting the number of complete cycles of a wave that pass through a particular point in one second and its unit is Hertz. One hertz equals one cycle per second. A 50 Hz signal means fifty complete cycles are completed every second.

Frequency determines how we perceive waves. The higher the frequency of a sound, the higher its pitch. The higher the frequency of light, the closer it is to the blue or violet end of the spectrum. Also, energy increases with increasing frequency; that's why ultraviolet light burns skin while radio waves pass through our bodies without harm.

The four dimensions that are associated with this calculation tool:

Frequency is one of a group of closely related wave quantities. Period is the time it takes for one complete cycle, wave speed is the rate at which the wave propagates, and wavelength is the distance between two points in phase, such as from one crest to the next. The table lists each quantity along with examples of their values.

Frequency formulas

These quantities are related by two equations. The first relates frequency and period; the second relates frequency to wavelength and wave speed.

By ordering these relationships, the remaining magnitudes can be determined. So if two arbitrary magnitudes are entered, they suffice to calculate the rest:

The angular frequency is a closely related quantity that is widespread in the fields of oscillations and alternating current. It indicates the speed with which the phase changes in radians per second:

Instructions for using this calculator

Enter the available values and set units. When enough information is entered, the remaining quantities will be immediately displayed with frequency being shown as the main result. It's not necessary to specify which values are to be calculated. The empty fields are those whose value is to be computed. If only period is entered, then frequency is calculated; if only frequency is entered, then period is calculated. To calculate wavelength or propagation speed, enter one of these quantities as a second input.

For light or electromagnetic waves, select the speed of light as your unit for wave velocity and enter either wavelength or frequency. When you open the range for electromagnetic waves, you can display the energy of photons and the spectral band to which this wave belongs. To convert revolutions per minute into hertz, set the unit of frequency to "cycles per minute" and read off the result in hertz.

Examples:

The following four examples show tasks that a frequency counting tool must handle in daily use.

Calculating frequency from period.

A signal repeats itself every 0.004 seconds. The frequency is then the inverse of the period:

Calculating period from frequency.

The frequency of the power grid in Europe is 50 hertz,

so the time for one period is:

The frequency is calculated from the wave speed and wavelength.

The speed of sound is about 343 meters per second. The frequency of a wave with a wavelength of 1.31 meters is:

This is close to middle C, the note at the centre of a piano keyboard.

To convert revolutions per minute to hertz:

A record player rotates at a speed of 45 revolutions per minute. Dividing by sixty gives the number of periods per second:

Frequency, wavelength, phase velocity

For a wave traveling at constant speed, frequency and wavelength are closely related. If the wavelength is doubled, then the frequency is halved. This is because more short waves or fewer long waves must pass your location in one second for the same speed. It is an inverse relationship where f equals v divided by λ, which also explains why deep bass notes have a longer wavelength than high-pitched whistling sounds.

The difference in the behavior of sound and light is only due to different speeds. The speed of sound in air is about 343 meters per second, so the wavelengths that are audible range from centimeters to meters. The propagation speed of light is about 300 million meters per second, so the wavelengths of visible light range from hundreds of nanometers while their frequencies range from hundreds of terahertz.

Frequency and energy of light

In light, the frequency is directly related to the energy of each photon. The Planck relation expresses this energy as a product of the Planck constant and the frequency:

The higher the frequency, the greater the energy of the photon. That is why ultraviolet and X-ray radiation can damage cells, while radio waves cannot. If you open up the "electromagnetic waves" section in a calculator tool, it will show the photon energy in electron volts. This is a convenient unit, with visible light being about 1.6 to 3.3 electron volts.

The same chart also shows the region of the electromagnetic spectrum to which each wave belongs. In ascending order of frequency these are: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.

Frequency and angular velocity

The normal frequency is the number of complete cycles per second and is measured in Hertz. Angular velocity measures the same motion as an angle and considers a full cycle to be two Pi radians. So its unit is radians per second which is equal to the value obtained by multiplying the frequency by two Pi. The angular velocity appears in equations for oscillations, waves and alternating current. In these equations phase is not followed as number of cycles but as an angle.

Applications of frequency

Frequency is relevant in almost all fields. In music and acoustics, frequency determines the pitch of a sound, with A being 440 hertz as standard. In optics, frequency determines the color of light. Radio, television, Wi-Fi, and cellular networks each use parts of the spectrum that are measured in kilohertz, megahertz or gigahertz. The mains electricity frequency is either 50 or 60 hertz, while computer clock speeds are in the gigahertz range. Rotating machines are usually quoted with a speed in revolutions per minute, which is actually the frequency in cycles per minute.

Tips for accurate results

Be sure to keep the wave speed accurate as this is necessary for determining the relationship between frequency and wavelength. For sound waves traveling through air at room temperature you can use about 343 meters per second. For electromagnetic waves use the speed of light. Be careful with units. Even if you enter the wavelength in nanometers and the wave speed in meters per second, the calculator will convert all values to base units first before calculating so that the frequency is given in hertz. At very fast or slow waves you can change the unit for frequency to kilohertz, megahertz, gigahertz or terahertz to keep the numbers readable.