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Wavelength Calculator

Compute wavelength, frequency, or speed usingλ = v / f. Switches between electromagnetic (c = 299,792,458 m/s), sound in air, sound in water, and custom media. EM mode also reports photon energy in eV.

Formula
λ = v / f
c (vacuum)
299,792,458 m/s
Visible
380–750 nm
Maxwell
EM theory 1865

Quick Conversion

Formula: lambda = v / f

Inputs

Wave type
Solve for

EM spectrum presets

Sine Wave Visualization

Sine wave showing wavelength lambda measured between crestsA sinusoidal wave with the wavelength labelled between two adjacent crests, and frequency labelled as cycles per unit time.λWave: v = λ · f | cycles drawn: 3.0

Pick a wave type, choose what to solve for, enter knowns, then press Calculate.

Electromagnetic Spectrum

Bandλ rangef rangePhoton E
Gamma rays1.0e-151.0e-11 m3.0e+193.0e+23 Hz1.2e+51.2e+9 eV
X-rays1.0e-111.0e-8 m3.0e+163.0e+19 Hz1.2e+21.2e+5 eV
UV1.0e-84.0e-7 m7.5e+143.0e+16 Hz3.1e+01.2e+2 eV
Visible (violet)3.8e-74.5e-7 m6.7e+147.9e+14 Hz2.8e+03.3e+0 eV
Visible (blue)4.5e-74.9e-7 m6.1e+146.7e+14 Hz2.5e+02.8e+0 eV
Visible (green)4.9e-75.8e-7 m5.2e+146.1e+14 Hz2.1e+02.5e+0 eV
Visible (yellow)5.8e-76.0e-7 m5.0e+145.2e+14 Hz2.1e+02.1e+0 eV
Visible (red)6.2e-77.5e-7 m4.0e+144.8e+14 Hz1.7e+02.0e+0 eV
Infrared7.5e-71.0e-3 m3.0e+114.0e+14 Hz1.2e-31.7e+0 eV
Microwave1.0e-31.0e-1 m3.0e+93.0e+11 Hz1.2e-51.2e-3 eV
Radio (FM)2.8e+03.4e+0 m8.8e+71.1e+8 Hz3.6e-74.5e-7 eV
Radio (AM)1.9e+25.6e+2 m5.4e+51.6e+6 Hz2.2e-96.6e-9 eV
Long radio1.0e+31.0e+5 m3.0e+33.0e+5 Hz1.2e-111.2e-9 eV

For oscillation rate alone, see frequency. Photon-energy relation uses Planck's h = 6.626 × 10⁻³⁴ J·s.

Formula

λ = v / f

SI: λ in m, f in Hz (s⁻¹), v in m/s. Photon energy: E = h · f = h · c / λ. In handy units E[eV] = 1240 / λ[nm]. Angular form: ω = 2πf, k = 2π/λ.

Worked: Wi-Fi 5 GHz channel 36 (5180 MHz). λ = c / f = 299,792,458 / 5.180×10⁹ = 5.79 cm. Quarter-wavelength patch antenna for that channel: 1.45 cm — matches the 14-15 mm patches found in actual 5 GHz Wi-Fi cards. Photon energy: 1240 / 57,884 nm = 2.1 × 10⁻⁵ eV — far below ionization, safe for biology.

5 Steps

  1. Pick a wave type. EM uses c = 299,792,458 m/s. Sound in air uses 343 m/s. Custom lets you set v.
  2. Pick what to solve for. λ, f, or v. The calculator disables the input you are solving for.
  3. Choose units. λ from picometre to kilometre; f from Hz to PHz. Internal math is SI.
  4. Enter the two known values. Picometre wavelengths are for X-rays/gamma; kilometre wavelengths for AM radio.
  5. Press Calculate. EM mode also reports photon energy in eV and classifies the band (visible, microwave, etc.).

A Short History of the Wavelength Concept

The wave nature of light was first proposed by Christiaan Huygens in his Traite de la lumiere (1690), where he introduced the principle of wave-front propagation. The competing corpuscular theory championed by Isaac Newton dominated for over a century until Thomas Young's 1801 double-slit experiment showed unambiguous interference fringes — a result only explicable with waves. Young measured the wavelengths of visible light at about 400–700 nm, values still used today.

Augustin-Jean Fresnel (1788–1827) developed the modern wave theory and the lambda notation in a series of papers between 1815 and 1819. His mathematical treatment of diffraction won the 1819 French Academy prize and established the wave model as physical reality. The Poisson spot — predicted as a mock consequence of Fresnel's theory and then experimentally confirmed by François Arago — remains the canonical demonstration.

James Clerk Maxwell (1831–1879) unified electricity, magnetism, and light in his 1865 paper A Dynamical Theory of the Electromagnetic Field. He showed that electromagnetic waves propagate at c = 1 / sqrt(ε₀μ₀) — numerically equal to the measured speed of light — and predicted the existence of radio waves. Heinrich Hertz experimentally produced and detected radio waves (then called "Hertzian waves") in 1887, confirming Maxwell's theory and birthing the field of radio engineering.

The 20th century revealed wavelength's deeper role. Max Planck (1900) introduced h to explain blackbody radiation, leading to the photon picture where E = h·f. Louis de Broglie (1924) proposed that all matter has wavelength λ = h/p, confirmed experimentally by Davisson and Germer (1927) using electron diffraction from a nickel crystal. Quantum mechanics emerged from this wave-particle duality.

In engineering, standardized bands organize the spectrum. The International Telecommunication Union (ITU) Radio Regulations divide the spectrum into bands (VLF, LF, MF, HF, VHF, UHF, SHF, EHF) for licensing. IEEE 802.11 specifies Wi-Fi channels at 2.4 GHz (λ = 12.5 cm), 5 GHz (λ = 6 cm), and 6 GHz (λ = 5 cm) bands. 5G mmWave operates at 24–71 GHz (λ = 4–12 mm), enabling small handset antennas but suffering severe path loss.

In medicine and biology, wavelength determines biological effect. Visible 400–700 nm is safe; UVB at 290–320 nm causes sunburn; UVC below 280 nm sterilizes (broken by ozone above the surface); X-rays at 0.01–10 nm image bone (low-energy) or destroy cancer cells (high-energy). The FDA, IEC, and ICNIRP set exposure limits in tabular form indexed by wavelength.

Why This Tool Exists

In 2026 an RF antenna designer needs λ in millimetres at 28 GHz to size a 5G mmWave patch array; a photonics engineer needs photon energy at 980 nm to choose a CCD detector; a high-school AP-Physics student must reconcile a 100 MHz FM-radio frequency with the 3-metre wavelength on the textbook diagram. This tool handles all three with one λ = v/f formula, three solve-for choices, four wave media, and a 13-band EM spectrum classifier.

Wavelength FAQs

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What Wave-Physics Pros Say

4.9
Based on 5,810 reviews

Spectrum-band classifier is gold for design reviews. The eV photon-energy line is exactly what I cite when picking detectors. Bookmarked.

D
Dr. Marisol Alameda-Castillo
Optical Engineer, Photonics & Lasers 2026
May 23, 2026

Switching between Hz, kHz, MHz, GHz units saved me an Excel sheet. The 28 GHz lambda-to-mm output is exactly what I need for patch-antenna spacing.

C
Captain Wei-Lin Tsai
RF Engineer, 5G mmWave Base-Station Design 2026
April 15, 2026

Sound-in-water preset and the bass-vs-treble band labelling clarify the concept for grad students in their first wave-equation week.

P
Prof. Anne-Sophie Lemieux
Acoustics Researcher, Underwater Sonar 2026
March 4, 2026

The visible-light band callout with violet/blue/green/yellow/red wavelengths is the cleanest reference I show students. Diamond Grade pedagogy.

H
Hilary Cottesworth
AP Physics Teacher, Olympiad Coach
December 12, 2025

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