Which formula is used?

The tool uses λ = v/f, where v = c/n. c is the speed of light in vacuum and n is the refractive index of the medium.

What if I only know frequency?

Enter frequency and select a medium; the tool computes wavelength in that medium and shows period, wavenumber, and photon energy.

Is atmospheric air treated as vacuum?

Air is very close to vacuum (n≈1.00027 at STP), but not exactly. Use the Air preset or set your own n.

Wavelength ↔ Frequency Calculator (with Medium)

Enter either wavelength or frequency, choose a medium (or set refractive index), then calculate. Private by design—everything runs locally in your browser.

Inputs

Wavelength (λ)

Symbol: λ. Provide λ or f (one is enough).

Frequency (f)

Symbol: f. Leave one of λ or f blank.

Medium (sets speed via refractive index n)

Wave speed: $ v = \dfrac{c}{n} $. Leave n empty to use the preset.

Results

Results will appear here.

Formulas Used

$ \lambda = \dfrac{v}{f} $
$ v = \dfrac{c}{n} $ (electromagnetic waves in a medium)
$ T = \dfrac{1}{f} $ (period)
$ k = \dfrac{2\pi}{\lambda} $ (wavenumber)
$ E = h f = \dfrac{h c}{\lambda} $ (photon energy)

Constants used: $ c = 299\,792\,458 \,\text{m·s}^{-1} $, $ h = 6.62607015\times 10^{-34}\,\text{J·s} $, $ 1\,\text{eV} = 1.602176634\times10^{-19}\,\text{J} $.

Understanding the Relationship

Wavelength $ (\lambda) $ and frequency $ (f) $ describe the same wave in different ways. They are tied together by the wave speed $v$: $ \lambda = v/f $. For electromagnetic waves (light, radio, microwaves), the speed in a material is $ v = \dfrac{c}{n} $, where $c$ is the speed of light in vacuum and $n$ is the material’s refractive index. That means when light enters a denser medium (larger $n$), the wavelength gets shorter while the frequency stays the same.

$$ \lambda = \frac{c}{n f} \quad\text{and}\quad f = \frac{c}{n \lambda} $$

In this calculator we also report the period $T = 1/f$, the wavenumber $k = 2\pi/\lambda$ (in rad·m$^{-1}$), and—for photons—the energy $E = h f = \dfrac{h c}{\lambda}$ (shown in joules and eV). These are convenient if you work in optics, RF, or photonics.

Quick intuition & everyday examples

Visible light. A green laser at $ \lambda \approx 532\,\text{nm} $ in air ($n \approx 1.00027$) has $ f \approx \dfrac{c}{n\lambda} \approx 5.63\times 10^{14}\,\text{Hz} $ (about 563 THz). Its photon energy is $E \approx 2.33\,\text{eV}$.
FM radio. A station at $100\,\text{MHz}$ ($1.0\times10^8\,\text{Hz}$) has wavelength $ \lambda \approx \dfrac{c}{n f} \approx 3.0\,\text{m} $ in air.
Wi-Fi / microwaves. At $2.4\,\text{GHz}$, $ \lambda \approx 12.5\,\text{cm} $ (in air). Higher frequency bands (e.g., $5\,\text{GHz}$) have proportionally shorter wavelengths.

Working across media

Because $ v = c/n $, choosing a medium (air, water, glass) or entering a custom $n$ simply scales the wavelength: $ \lambda_{\text{medium}} = \lambda_0 / n $. Frequency does not change at an interface, which is why color (set by $f$) is preserved when light passes from air into glass—only the spacing between wave crests changes inside the material.

Units, ranges, and tips

Common wavelength units are nm, μm, mm, cm, and m; frequency is typically Hz, kHz, MHz, GHz, or THz. Visible light spans roughly $400\text{–}700\,\text{nm}$ ($\approx 430\text{–}750\,\text{THz}$); infrared is longer wavelengths (lower $f$), ultraviolet is shorter (higher $f$). Radio covers kHz to tens of GHz with wavelengths from kilometers to millimeters. The calculator auto-scales results to readable units, and it uses exact CODATA constants: $ c = 299{,}792{,}458\,\text{m·s}^{-1} $ and $ h = 6.62607015\times10^{-34}\,\text{J·s} $.

When precision matters

Real materials are dispersive: $n$ depends on wavelength and temperature. Our presets (air $\approx 1.00027$, water $\approx 1.333$, typical crown glass $\approx 1.517$) are great for estimates; for lab-grade work, enter your own $n$ at the operating wavelength. Finally, note that the formulas here apply to electromagnetic waves. For sound or water waves you would use the appropriate wave speed $v$ for that medium, not $c/n$.

5 Fun Facts about Waves

Vacuum is barely beatable

Air slows light by only ~0.027% versus vacuum. Glass can chop speed to about 2/3 of c, shrinking wavelengths inside it.

Speed limit

Red bends less than blue

Higher-frequency (blue) light sees a slightly higher refractive index, so it refracts more. That dispersion spreads white light into rainbows.

Color split

Wi‑Fi wiggles around walls

At 2.4 GHz the wavelength is ~12.5 cm—long enough to diffract through door gaps and around corners, unlike short-wavelength visible light.

Everyday diffraction

X-rays match atom spacing

Typical X-rays are ~0.1 nm long—on the order of atomic lattice spacing—letting them reveal crystal structures via diffraction.

Tiny rulers

Radio can stretch for kilometers

Low-frequency radio waves can be kilometers long, bouncing off the ionosphere to travel far beyond line-of-sight horizons.

Long-haul waves

Frequently Asked Questions

Does the wavelength change in a medium?

Yes. Frequency stays the same when entering a medium, but wavelength becomes shorter by a factor of $n$: $ \lambda_{\text{medium}} = \lambda_0 / n $.

Which units are supported?

Wavelength: nm, μm, mm, cm, m. Frequency: Hz, kHz, MHz, GHz, THz. The tool auto-scales output for readability.

What is “wavenumber”?

Wavenumber $k$ measures how rapidly a wave oscillates in space: $k=2\pi/\lambda$ (in rad/m).

Is the refractive index constant?

In reality, $n$ depends on wavelength and temperature. For quick estimates, these presets are fine; for precision work, enter your own $n$.

Is my data private?

Yes—everything runs locally in your browser; nothing is uploaded.