Wavelength Calculator

Wavelength Calculator for light, radio and sound. Enter a frequency, photon energy or wavenumber to get λ and the quarter wave in a vacuum, air, water, coax, a PCB or a dielectric.

Wavelength Calculator for Any Wave

The Wavelength Calculator works for light, radio and sound because every wave follows the same rule. Wavelength is the wave’s speed divided by its frequency, so the only thing that changes from case to case is the speed the wave travels at.

Pick what you want in the Calculate menu, then pick the medium. The tool sets the wave speed for that medium, and typing your own value in Wave Velocity switches it to a custom speed.

Besides wavelength from frequency, the menu finds wavelength from a period, a photon energy or a wavenumber. It also turns a wavelength back into a frequency, and works out the wave speed from a measured wavelength and frequency.

Wavelength Formula

Wavelength λ is the distance from one crest of a wave to the next. Speed v is how far the wave travels each second, and frequency f is how many crests pass each second. Divide one by the other and you get the length of each cycle.

$$\lambda = \frac{v}{f}$$

$$f = \frac{v}{\lambda}$$

The default case is a 2.45 GHz Wi-Fi or microwave oven signal in free space. Dividing 299,792,458 m/s by 2.45 × 10⁹ Hz gives 0.1224 m, so each wave is 12.24 cm long. Switch to Frequency from Wavelength and the same formula runs backward, so 500 nm green light comes out at 599.6 THz.

Two more forms of the same rule cover the other modes. When you know the period T of one cycle, wavelength is speed times that time. When you have measured both λ and f, their product gives the wave speed.

$$\lambda = v T, \quad v = \lambda f$$

A sound with a 2.5 ms period repeats 400 times a second, so in 20 °C air its wavelength is 343.2 × 0.0025 = 85.80 cm. In Wave Velocity from λ and f, the defaults of 12.2 cm at 2.45 GHz give 298,900 km/s, which tells you the measured wave is very close to light speed.

Wavelength and frequency are inversely proportional. Double the frequency and the wavelength halves, which is what the Wavelength at Other Frequencies table under the results shows for your own medium.

The speed of light used here is the exact SI value from the NIST CODATA constants. The Planck constant and the elementary charge used for photon energy are also exact SI values from the same source.

Wavelength Calculator for RF

As a wavelength calculator for RF work, the tool gives the full wave and the cut lengths that antennas and stubs are built from. The first card shows the quarter wave (λ/4), the half wave (λ/2) and the 5/8 wave, which is the 1/4 wavelength calculator job people search for.

The first three columns are free-space lengths. A real wire antenna resonates a little short of its half wave, so for free-space signals up to 3 GHz the first card swaps the 5/8 wave row for a dipole cut length.

That row uses the ARRL Antenna Book rule of 468 ÷ f in MHz, giving feet, which is about 95% of the half wave. A 14.2 MHz dipole comes out at 32.96 ft, or 10.05 m. Treat it as a starting length and trim on test with an SWR meter, since wire size and nearby objects shift the exact point.

The second card adds the period of one cycle and the angular wavenumber. At 2.45 GHz the period is 408.2 ps and k = 2π ÷ λ = 51.35 rad/m, the figure wave equations use. For the related ω = 2πf, the Angular Frequency Calculator converts hertz to rad/s.

Wavelength in Dielectric, Coax and PCB

A wave keeps its frequency when it enters a material, but it slows down. Because λ = v ÷ f, a slower wave packs each cycle into a shorter length. That shorter length is what sets stub lengths, phasing lines and trace lengths in real circuits.

$$\lambda = \frac{\lambda_0}{\sqrt{\varepsilon_r}} = \frac{\lambda_0}{n}$$

Here λ₀ is the free-space wavelength and εr is the dielectric constant. As a wavelength calculator in dielectric material, a 1 GHz signal in FR-4 with εr = 4.4 has a wavelength of 14.29 cm, against 29.98 cm in free space. Stripline traces sit fully inside the board, so the Dielectric material option with the board εr gives their wavelength directly.

Coax cable works the same way through its velocity factor. A cable with a 66% velocity factor carries a 146 MHz signal at 0.66 × c, so the wavelength in the cable is 1.355 m and a quarter-wave stub is 33.88 cm. The fourth card shows the delay this adds, 5.054 ns per meter against 3.336 ns per meter in free space.

Wavelength Calculator for PCB Traces

A microstrip trace runs on the board surface, so part of its field sits in the air above. The wave sees an effective εr between 1 and the board value. The PCB option works it out with Hammerstad’s microstrip formula from the trace width w and the board height h.

$$\varepsilon_{eff} = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r – 1}{2} \left(1 + \frac{12h}{w}\right)^{-1/2}$$

The default board is 1.6 mm FR-4 with εr = 4.4 and a 3 mm trace. That gives εeff = 3.325, so a 2.45 GHz signal has a 6.711 cm wavelength on the trace.

If the whole field sat inside the board it would be 5.833 cm, which shows how much the air above matters. For narrow traces where w is less than h, the tool adds the formula’s 0.04(1 − w/h)² correction, and trace thickness is not counted.

Guide Wavelength in a Waveguide

Inside a hollow rectangular waveguide, the TE10 wave zigzags between the side walls. Its guide wavelength λg is longer than in free space, and nothing travels at all below the cutoff frequency set by the wide inner wall a.

$$\lambda_g = \frac{\lambda_0}{\sqrt{1 – (f_c / f)^2}}, \quad f_c = \frac{c}{2a}$$

The default is WR-340 guide with a = 86.36 mm, the size used around 2.45 GHz. Its cutoff is 1.736 GHz, so at 2.45 GHz the guide wavelength is 17.34 cm against 12.24 cm in free space. The fourth card shows the cutoff, the 424,800 km/s phase velocity and the 211,600 km/s group velocity, and their product always equals c².

A frequency below the cutoff is flagged with the cutoff value, since the wave dies out instead of traveling. Frequency from Wavelength also works in this medium, so a measured λg gives the frequency that produced it.

Sound Wavelength Calculator

Pick a sound medium and the Wavelength Calculator becomes a sound wavelength tool. Sound moves close to a million times slower than light, so the same frequency gives a far shorter wave, and audio wavelengths run from centimeters to many meters.

$$v = 331.3 \sqrt{1 + \frac{T}{273.15}}$$

Speed in air depends on temperature T in °C, following the ideal-gas form in OpenStax University Physics, section 17.2. It gives 343.2 m/s at 20 °C and 354.7 m/s at 40 °C, about 0.6 m/s more for each degree. Speed in water uses the Marczak equation, valid from 0 to 95 °C as listed by the UK National Physical Laboratory, and gives 1,482.4 m/s at 20 °C.

The table works the frequency to wavelength calculator sound case for both media at 20 °C. Sound in water travels 4.32 times faster than in air, so every wavelength is 4.32 times longer.

For sound, the cards switch to audio use. The first card gives the quarter and half wave used for room modes, bass traps and speaker spacing. The third card names the nearest musical note to your frequency, tuned to A4 = 440 Hz, and how many cents it is off. The fourth card gives the delay per meter, which is 2.914 ms in 20 °C air.

Wavelength From Energy and Wavenumber

The wavelength calculator from energy mode turns a photon energy into its vacuum wavelength. A photon’s energy is Planck’s constant times its frequency, so wavelength equals hc divided by the energy.

$$\lambda = \frac{h c}{E}$$

With E in electronvolts and λ in nanometers, hc works out to 1,239.84 eV·nm. So a 2.5 eV photon has a wavelength of 1,239.84 ÷ 2.5 = 495.9 nm, which the third card places in the visible green band. Energy can also be entered in J, meV, keV, MeV or kJ/mol, and 2.5 eV equals 241.2 kJ/mol.

The wavenumber mode serves spectroscopy, where lines are quoted in cm⁻¹. Wavelength is simply one over the wavenumber, so 1,000 cm⁻¹ gives 10 µm in the infrared. Choose the rad/m unit instead to enter an angular wavenumber k, and the tool uses λ = 2π ÷ k.

$$\lambda = \frac{1}{\tilde{\nu}} = \frac{2 \pi}{k}$$

Both of these modes give the vacuum wavelength. Tables of spectral lines longer than 200 nm are often listed in standard air, as NIST’s atomic spectroscopy notes explain, and an air wavelength is about 0.03% shorter.

Wavelength Ranges of the Spectrum

For light and radio, the third card names the band of the electromagnetic spectrum your wave falls in. It always uses the free-space wavelength, so light slowed in glass keeps its true color name. Band edges are conventions and different references move them slightly.

Light in water shows why the free-space value is used. A 500 nm green beam in water has a wavelength of only 375.1 nm, yet its frequency stays 599.6 THz and it still looks green. The eye responds to frequency, not to the shortened wavelength inside the water.

Wavelength Calculator FAQ

These answers cover common questions about wavelength in physics, radio and sound. Each one uses the same speeds and constants as the Wavelength Calculator above.

How do you calculate wavelength?

Divide the wave’s speed by its frequency. Use 299,792,458 m/s for light or radio in free space and about 343 m/s for sound in room-temperature air. Keep the units matched, so meters per second divided by hertz gives meters. For a 1 kHz tone in air that is 343.2 ÷ 1,000 = 0.3432 m.

What is the wavelength of 2.4 GHz Wi-Fi?

At 2.4 GHz the free-space wavelength is 12.49 cm, and at the 2.45 GHz band center it is 12.24 cm. The quarter wave is about 3.1 cm, which is why 2.4 GHz antennas are only a few centimeters long. The 5 GHz band has wavelengths near 6 cm, about half as long.

Why does wavelength get shorter in water or glass?

A wave slows down inside a denser medium while its frequency stays fixed by the source. Since λ = v ÷ f, the wavelength drops by the same factor as the speed. Light in water with n = 1.333 travels at 75% of its vacuum speed, so its wavelength shrinks to 75% too.

Which has a longer wavelength, red or blue light?

Red light has the longer wavelength, roughly 620 to 750 nm, while blue sits near 450 to 495 nm. Because wavelength and frequency are inversely related, blue light has the higher frequency and more energy per photon. A 450 nm blue photon carries 2.76 eV, against 1.77 eV for a 700 nm red photon.

What units is wavelength measured in?

The SI unit is the meter, but each field uses a convenient size. Radio uses meters and centimeters, PCB and microwave work uses millimeters or mils, and light uses nanometers or micrometers. X-rays are often given in picometers or angstroms, where 1 Å is 0.1 nm, and all of these are in the Result Unit menu.

How is wavelength related to the wave equation?

A traveling wave is written y(x, t) = A sin(kx − ωt), where k = 2π ÷ λ and ω = 2πf. The ratio ω ÷ k gives the wave speed back, so λ, f and v are tied together in every wave equation. The Harmonic Wave Equation Calculator uses these values to find the displacement at any point and time.

To go the other way and find frequency from a period, a cycle count or rpm, use the Frequency Calculator. For the oscillation behind a wave, see the Simple Harmonic Motion Calculator or browse all the Rotational Motion Calculators.