Frequency to Wavelength Converter
Our free signal & frequency converter handles frequency wavelength conversions. See tables, ratios, and examples for quick reference.
Frequency to Wavelength Converter
Calculator
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Formula: Wavelength (lambda) = Speed of wave (v) / Frequency (f)
Worked example โ 100 MHz = 2.998 m wavelength (Radio Wave band)
Formula
Wavelength (lambda) = Speed of wave (v) / Frequency (f)
Divide the speed of the wave by its frequency. In vacuum, the speed is 299,792,458 m/s. In other media, divide the vacuum speed by the refractive index. Wave number is the reciprocal of wavelength.
Worked Examples
Example 1: FM Radio Station Wavelength
Problem:What is the wavelength of a 100 MHz FM radio signal in air?
Solution:Wavelength = speed of light / frequency lambda = 299,792,458 / 100,000,000 lambda = 2.998 meters
Result:100 MHz = 2.998 m wavelength (Radio Wave band)
Example 2: 5G Cellular Wavelength
Problem:Calculate the wavelength of a 28 GHz 5G mmWave signal.
Solution:Wavelength = 299,792,458 / (28 * 10^9) lambda = 299,792,458 / 28,000,000,000 lambda = 0.01071 meters = 10.71 mm
Result:28 GHz = 10.71 mm wavelength (Microwave band)
Frequently Asked Questions
How do you convert frequency to wavelength?
Wavelength equals the speed of the wave divided by its frequency, expressed as lambda = v / f. For electromagnetic waves in a vacuum, v is the speed of light (299,792,458 m/s). For example, an FM radio station at 100 MHz has a wavelength of 299,792,458 / 100,000,000 = 2.998 meters. In other media like water or glass, the speed is reduced by the refractive index, producing shorter wavelengths.
Does wavelength change in different media?
Yes, wavelength changes when a wave enters a different medium because the wave speed changes while the frequency stays constant. The speed in a medium equals the speed of light divided by the refractive index (n). For example, light in glass (n = 1.5) travels at 2/3 the speed of light, so its wavelength is also 2/3 of what it would be in vacuum. This principle is fundamental to optics, fiber communications, and lens design.
What is the electromagnetic spectrum?
The electromagnetic spectrum spans all possible wavelengths and frequencies of electromagnetic radiation. It ranges from radio waves (wavelengths of kilometers) through microwaves, infrared, visible light (380-700 nm), ultraviolet, X-rays, to gamma rays (wavelengths smaller than atoms). All electromagnetic waves travel at the speed of light in vacuum, so higher frequency always means shorter wavelength.
What is a wave number and how is it used?
Wave number (k) is the spatial frequency of a wave, defined as the number of wavelengths per unit distance. It equals 1 divided by the wavelength (k = 1/lambda) in cycles per meter, or 2*pi/lambda in radians per meter. Wave number is widely used in spectroscopy, quantum mechanics, and crystallography because it is directly proportional to energy and momentum of photons.
Why is the speed in air set slightly below the vacuum speed of light?
Air has a refractive index just above one, close to 1.0003 at optical frequencies and standard conditions. Dividing 299,792,458 m/s by 1.0003 gives about 299,702,547 m/s, the value this tool uses for air. The resulting wavelength is only about 0.03 percent shorter than in vacuum, which is negligible for radio antenna work but does matter for interferometry and precise laser metrology, where the index also shifts with pressure and humidity.
How do you size an antenna from the wavelength you calculated?
Antenna elements are cut as simple fractions of the wavelength. A half-wave dipole is about lambda / 2 long and a ground-plane whip is about lambda / 4. At 100 MHz the free-space wavelength is 2.998 m, so a quarter-wave element is roughly 75 cm. Real elements come out a few percent shorter because the velocity factor of the conductor and end effects at the tips slow the wave slightly, so builders cut long and trim to resonance.
How does the wave number here relate to the cm-1 used in spectroscopy?
This tool reports wave number as one divided by the wavelength in metres. Infrared spectroscopy uses reciprocal centimetres instead, so 1 cm-1 equals 100 m-1. A band at 1,000 cm-1 corresponds to a wavelength of 10 micrometres and a frequency near 30 THz. Spectroscopists favour cm-1 because it is directly proportional to photon energy, which puts vibrational modes on a linear energy axis instead of a reciprocal wavelength axis.
How do you get photon energy from a frequency or wavelength?
Photon energy is E = h x f, or equivalently E = h x c / lambda, where h is the Planck constant of 6.62607015 x 10^-34 J s. In practical units the shortcut is E in electronvolts equals about 1,240 divided by the wavelength in nanometres. Green light near 500 nm therefore carries about 2.48 eV per photon. This is why short-wavelength ultraviolet can break chemical bonds while long-wavelength infrared mainly deposits heat.
Is the refractive index of water really 1.333 at every frequency?
No. The 1.333 figure applies to visible light, and even there it drifts slightly across the spectrum, an effect called dispersion that is what splits white light into a rainbow through a prism. At radio and microwave frequencies water behaves very differently, with a static relative permittivity near 80 that corresponds to an effective index close to 9. Use the custom speed option whenever you are working far from the visible band.
What does the period output add on top of the wavelength?
Period is the time for one cycle, T = 1 / f, while wavelength is the distance covered in that same cycle. The two are tied together by lambda = v x T, so the wavelength is simply the propagation speed multiplied by the period. Seeing both is useful when you move between a time-domain view on an oscilloscope, where you measure the period directly, and a spatial view such as antenna spacing or optical path length.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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