Wavelength, Frequency & Photon Energy Calculator

About the Wavelength, Frequency & Photon Energy Calculator

Every wave obeys v = f λ: speed equals frequency times wavelength. For light and every other electromagnetic wave the speed in vacuum is exactly c = 299,792,458 m/s, and each photon carries an energy E = h f = hc ÷ λ. Type any one of wavelength, frequency, period, wavenumber or photon energy and the calculator gives all the others — energy in joules, electronvolts and kJ per mole of photons — plus the photon momentum, the equivalent temperature E/k and, with a power, the number of photons per second.

It names the part of the spectrum using the ISO 21348 categories (gamma rays to radio, with UV-A/B/C and IR-A/B/C) and, for radio frequencies, the ITU band (VHF, UHF, SHF…). Visible wavelengths come with an approximate colour swatch. Choose a medium — water, glass, diamond or a refractive index or dielectric constant of your own — to get the wavelength and speed inside it. A Sound mode does the same for sound in air at any temperature or in other materials, and names the nearest musical note.

Common uses

• Physics and chemistry homework: λ, f and E = hf in any units, with the working.
• Spectroscopy: converting between nm, cm⁻¹, eV and kJ/mol.
• Lasers and LEDs: photon energy and photons per second from the power.
• Radio and antennas: wavelength of a frequency in air or along a cable dielectric.
• Acoustics and music: the wavelength of a note in air, water or steel.

The formulas

• Wave equation: v = f λ, T = 1/f, ω = 2πf.
• In a medium: v = c/n and λ_medium = λ_vacuum/n; the frequency does not change. For a non-magnetic material n = √ε_r.
• Photon energy: E = h f = hc/λ, so E (eV) = 1,239.84 ÷ λ (nm). Per mole of photons multiply by N_A = 6.02214076 × 10²³.
• Wavenumber: ν̃ = 1/λ (vacuum), usually in cm⁻¹.
• Photon momentum: p = h/λ (vacuum); equivalent temperature: E/k.
• Sound in air: v = 331 m/s × √(1 + T/273 °C) — 343 m/s at 20 °C.

c, h, e, N_A and k are exact defined constants of the SI.

Band names and their limits

Bands are named by vacuum wavelength with ISO 21348:2007: gamma rays below 1 pm; X-rays 1 pm–10 nm (hard below 0.1 nm, soft above); ultraviolet 10–400 nm (EUV 10–121 nm, FUV 122–200 nm, UVC 100–280 nm, UVB 280–315 nm, UVA 315–400 nm); visible 380–760 nm (purple/violet 360–450, blue 450–500, green 500–570, yellow 570–591, orange 591–610, red 610–760 nm); infrared 760 nm–1 mm (IR-A to 1.4 µm, IR-B to 3 µm, IR-C beyond); microwaves 1–15 mm; radio 0.1 mm–100 m. Radio frequencies also get their ITU-R V.431 band number: band N runs from 0.3 × 10ᴺ to 3 × 10ᴺ Hz (band 8, VHF, is 30–300 MHz).

These limits are conventions and other references draw them differently — OpenStax, for example, gives visible light as about 400–750 nm and UV-A as 320–400 nm. Physicists also often call photons from atomic nuclei gamma rays whatever their wavelength.

About the colour swatch

The swatch converts the wavelength to CIE 1931 XYZ with the analytic fit of Wyman, Sloan and Shirley (2013) and then to sRGB. Pure spectral colours are more saturated than any screen can show, so channels that would be negative are set to zero and the colour is shown at full brightness. Below about 420 nm and above about 650 nm the hue of spectral light hardly changes (the ends of the CIE spectral locus), so those wavelengths share the violet or red of the nearest end. Real light near the ends of the spectrum looks much dimmer: the eye’s sensitivity, shown as an approximate percentage, falls from its peak near 555 nm.

Sources

• BIPM, The International System of Units (SI Brochure, 9th ed., 2019): exact c, h, e, N_A and k; NIST CODATA 2022 values.
• ISO 21348:2007, Space environment — Process for determining solar irradiances, spectral categories (definitions as published by Space Environment Technologies).
• ITU, Recommendation ITU-R V.431-8 (08/2015), nomenclature of frequency and wavelength bands.
• OpenStax, University Physics Volume 3: §1.1 The Propagation of Light (Table 1.1, refractive indices at 589 nm); Volume 2: §8.5 (Table 8.1, dielectric constants) and §16.5 The Electromagnetic Spectrum; Volume 1: §17.2 Speed of Sound (Table 17.1, Eq. 17.7, Example 17.1).
• OpenStax, College Physics 2e, §17.6 Hearing: human hearing 20–20,000 Hz, infrasound and ultrasound.
• ISO 16:1975, Acoustics — Standard tuning frequency: A = 440 Hz.
• C. Wyman, P.-P. Sloan and P. Shirley, “Simple Analytic Approximations to the CIE XYZ Color Matching Functions”, Journal of Computer Graphics Techniques 2(2), 2013; W3C CSS Color Module Level 4 (XYZ to sRGB).

Limitations

• Refractive indices are for 589 nm light; at other wavelengths n differs slightly (dispersion), and absorbing materials need a complex index.
• Dielectric constants are low-frequency values at room temperature; at high frequencies many materials (water especially) respond differently.
• The speed of sound in air uses the textbook formula for dry air; humidity and pressure changes are ignored. Speeds in liquids and solids are fixed table values.
• Colour swatches are approximations — screens cannot show pure spectral colours.
• Band names are conventions with overlapping or differing limits between standards.

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