Convert wavelength to frequency, frequency to wavelength, calculate photon energy from wavelength, energy to wavelength, wave speed, and wavenumber — all 5 modes for light, sound, radio waves, and the full electromagnetic spectrum.
✓ Verified: NIST CODATA 2022 Physical Constants
Enter the wavelength valueEnter a valid wavelength.
Select unit for your wavelengthSelect a unit.
Wave propagation mediumSelect a medium.
Enter wave speed in m/sEnter a valid speed.
Enter the frequency valueEnter a valid frequency.
Select the frequency unitSelect a unit.
Wave propagation mediumSelect a medium.
Enter speed in m/sEnter a valid speed.
Wavelength of the photonEnter a valid wavelength.
Select wavelength unitSelect a unit.
Energy of the photonEnter a valid energy.
Select the energy unitSelect a unit.
Frequency in hertzEnter a valid frequency.
Wavelength in metersEnter a valid wavelength.
Result
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⚠️ Disclaimer: Calculations use NIST CODATA 2022 constants (c = 299,792,458 m/s, h = 6.62607015 × 10²³&sup4; J·s). For vacuum EM waves only unless a specific medium is selected.
📚 Sources & Methodology
All calculations use the following verified constants and sources:
NIST CODATA 2022 — Speed of light c = 299,792,458 m/s (exact), Planck's constant h = 6.62607015 × 10²³&sup4; J·s
NIST Standard Reference Data — Electromagnetic spectrum ranges, wave speed in media
ISO 80000-7:2019 — Quantities and units for light and radiation
Griffiths, Introduction to Electrodynamics, 4th Ed. — Wave equations and photon energy formulas
Complete Guide to Wavelength Calculations
The Fundamental Wave Equation: v = fλ
Every wavelength calculation starts from one equation: wave speed equals frequency times wavelength. This relationship is universal — it applies to light, sound, radio waves, water waves, and all other wave phenomena. The three variables are completely interchangeable: knowing any two lets you calculate the third.
Core Wave Equations
v = f × λ (wave speed = frequency × wavelength)λ = v / f (wavelength = speed / frequency)f = v / λ (frequency = speed / wavelength)For EM waves: λ = c / f (c = 299,792,458 m/s in vacuum)Period: T = 1/f = λ/v (seconds per cycle)
Wavelength to Frequency Conversion
To convert wavelength to frequency for electromagnetic waves, divide the speed of light (c = 299,792,458 m/s) by the wavelength in meters. For a 500 nm green laser: f = 299,792,458 / (500 × 10²&sup9;) = 5.996 × 10¹&sup4; Hz (599.6 THz). For a 3-meter FM radio wave: f = 299,792,458 / 3 = 99.9 MHz. For sound: use the speed of sound in your medium (343 m/s in air at 20°C).
Photon Energy from Wavelength: E = hc/λ
A photon's energy is inversely proportional to its wavelength — shorter wavelength means higher frequency means higher energy. The 1240 eV·nm shortcut is extremely useful: divide 1240 by the wavelength in nanometers to get energy in electron volts. A 400 nm UV photon has 1240/400 = 3.10 eV. A 700 nm red photon has 1240/700 = 1.77 eV. A 0.1 nm X-ray photon has 12,400 eV = 12.4 keV.
Photon Energy Formula
E = h × f = h × c / λh = 6.62607015 × 10^-34 J·s (Planck's constant, CODATA 2022)Shortcut: E (eV) = 1240 / λ (nm) [for visible and UV light]Example: 500 nm green photon: E = 1240/500 = 2.48 eV = 3.97 × 10^-19 J
Wavenumber: Spatial Frequency
Wavenumber describes how many wave cycles fit per unit of distance. Angular wavenumber k = 2π/λ is measured in radians per meter and appears in wave equations as e^(ikx). Spectroscopic wavenumber ν̃ = 1/λ (in cm²¹) is used in IR and Raman spectroscopy to identify molecular bonds. A 10 μm IR photon has spectroscopic wavenumber = 1/(10 × 10²&sup4; cm) = 1,000 cm²¹.
Electromagnetic Spectrum — Wavelength Reference
Type
Wavelength
Frequency
Photon Energy
Examples
Gamma rays
<0.01 nm
>30 EHz
>124 keV
Nuclear reactions, PET scans
X-rays
0.01–10 nm
30 PHz–30 EHz
124 eV–124 keV
Medical imaging, security
Ultraviolet
10–380 nm
790 THz–30 PHz
3.3–124 eV
Sterilization, tanning
Violet
380–450 nm
665–789 THz
2.76–3.26 eV
Visible light
Blue
450–495 nm
606–668 THz
2.51–2.76 eV
Visible light
Green
495–570 nm
526–606 THz
2.18–2.50 eV
Visible light
Yellow/Orange
570–620 nm
484–526 THz
2.00–2.18 eV
Visible light
Red
620–750 nm
400–484 THz
1.65–2.00 eV
Visible light
Near infrared
750 nm–2.5 μm
120–400 THz
0.5–1.65 eV
TV remotes, fiber optics
Thermal IR
2.5–1000 μm
300 GHz–120 THz
1.2 meV–0.5 eV
Heat imaging, lasers
Microwave
1 mm–30 cm
1–300 GHz
4 μeV–1.2 meV
WiFi, 5G, radar
Radio (UHF/VHF)
10 cm–10 m
30 MHz–3 GHz
0.12–12 μeV
TV, FM, mobile
Radio (AM)
100 m–10 km
30–3,000 kHz
0.12–12 neV
AM broadcast
Sound Wavelength vs EM Wavelength
Sound waves are mechanical pressure waves requiring a medium. Their speed depends entirely on the medium: 343 m/s in air (20°C), 1,481 m/s in water, 5,120 m/s in steel. The human auditory range (20 Hz – 20 kHz) corresponds to wavelengths of 17.2 m (bass, 20 Hz) down to 1.7 cm (treble, 20 kHz) in air. This matters for speaker design: large woofers are needed for long-wavelength bass; small tweeters for short-wavelength treble.
Wavelength and Antenna Design
Antennas are sized as fractions of the signal wavelength. A half-wave dipole antenna has length λ/2. A quarter-wave monopole has length λ/4. For FM radio at 100 MHz (λ = 3 m): dipole length = 1.5 m. For WiFi at 2.4 GHz (λ = 12.5 cm): dipole = 6.25 cm. For 5G mmWave at 28 GHz (λ = 10.7 mm): dipole = 5.35 mm. Massive MIMO arrays at 5G use hundreds of these tiny antennas in a single panel.
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Quick conversions to memorize: WiFi 2.4 GHz = 12.5 cm wavelength. WiFi 5 GHz = 6.0 cm. 5G 28 GHz = 1.07 cm. FM radio at 100 MHz = 3.0 m. Green laser 532 nm = 564 THz. Human body temperature radiates peak IR at 9.3 μm = 32 THz.
❓ Frequently Asked Questions
Wavelength = wave speed / frequency (λ = v/f). For EM waves in vacuum: λ = c/f = 299,792,458 / frequency (Hz). For 100 MHz FM: λ = 299,792,458 / 100,000,000 = 2.998 m. For sound at 440 Hz in air: λ = 343 / 440 = 0.780 m. Use the Frequency to Wavelength tab above for instant conversion.
Frequency = wave speed / wavelength (f = v/λ). For light: f = 299,792,458 / λ (in meters). For 500 nm green light: f = 299,792,458 / (500 x 10^-9) = 5.996 x 10^14 Hz = 599.6 THz. Remember to convert wavelength to meters first before dividing.
E = h x c / λ, where h = 6.626 x 10^-34 J*s and c = 299,792,458 m/s. The shortcut for visible light: E (eV) = 1240 / λ (nm). A 450 nm blue photon = 1240/450 = 2.76 eV. A 632 nm red laser = 1240/632 = 1.96 eV. Shorter wavelength always means higher photon energy.
Wavenumber is the spatial frequency of a wave. Angular wavenumber k = 2*pi / λ (rad/m). Spectroscopic wavenumber = 1/λ (cm^-1). A 10 μm mid-IR photon has spectroscopic wavenumber = 1/(10 x 10^-4 cm) = 1,000 cm^-1. IR spectroscopy identifies molecular bonds by their characteristic wavenumber absorption peaks.
Visible light spans approximately 380 to 700 nm. Violet 380-450 nm (750-665 THz). Blue 450-495 nm (665-605 THz). Green 495-570 nm (605-526 THz). Yellow 570-590 nm (526-508 THz). Orange 590-620 nm (508-484 THz). Red 620-750 nm (484-400 THz). Below 380 nm is UV (invisible). Above 750 nm is infrared (invisible but felt as heat).
AM radio 540-1700 kHz = 176-556 meter wavelengths. FM radio 87.5-108 MHz = 2.78-3.43 m. WiFi 2.4 GHz = 12.5 cm. WiFi 5 GHz = 6.0 cm. 4G LTE 700 MHz = 42.8 cm. 5G sub-6GHz = 5-30 cm. 5G mmWave 28 GHz = 1.07 cm. Higher frequency = shorter wavelength = more data capacity but less penetration through walls.
Longer wavelengths penetrate obstacles better and diffract (bend) more around corners. AM radio at 300 m wavelength easily diffracts over hills and buildings. 5G at 1 cm wavelength is blocked by most walls. X-rays at 0.1 nm pass through soft tissue but are absorbed by bone. Sound at 17 m (20 Hz bass) passes through walls; 1.7 cm (20 kHz treble) is easily absorbed.
The de Broglie wavelength: λ = h / (m x v), where h = 6.626 x 10^-34 J*s, m = mass in kg, v = velocity in m/s. An electron (m = 9.11 x 10^-31 kg) at 10^6 m/s: λ = 6.626x10^-34 / (9.11x10^-31 x 10^6) = 0.727 nm. This is comparable to atomic spacing, which is why electrons can diffract through crystals and why electron microscopes resolve atomic structure.
Antenna length is typically λ/4 (quarter-wave monopole) or λ/2 (half-wave dipole). For maximum efficiency, antenna size must match signal wavelength. FM at 100 MHz (λ = 3m): ideal dipole = 1.5 m. GPS at 1575 MHz (λ = 19 cm): ideal element = 9.5 cm. Bluetooth 2.4 GHz (λ = 12.5 cm): PCB antenna = ~3 cm. This is why 5G millimeter wave antennas can fit entirely inside a smartphone chip.
In air at 20 degrees C (v = 343 m/s): 20 Hz = 17.15 m, 100 Hz = 3.43 m, 440 Hz (concert A) = 0.780 m, 1,000 Hz = 0.343 m, 5,000 Hz = 6.86 cm, 20,000 Hz = 1.72 cm. In water (1,481 m/s): same frequencies give wavelengths 4.3x longer. In steel (5,120 m/s): 14.9x longer. Speed varies with temperature: +0.6 m/s per degree C in air.
Wavelength (nm) = 1240 / Energy (eV) for photons. This shortcut comes from E = hc/λ with h and c combined: 1240 eV*nm. A 3.0 eV photon: λ = 1240/3.0 = 413 nm (violet). A 1.8 eV photon: λ = 1240/1.8 = 689 nm (red). A 100 eV X-ray: λ = 1240/100 = 12.4 nm (soft X-ray). Use the Energy to Wavelength tab above for any value.
Wavelength (λ, meters) is the spatial distance between wave peaks. Period (T, seconds) is the time between peaks. They relate as: λ = v x T = v/f. A 1,000 Hz sound: T = 0.001 s, λ = 343 x 0.001 = 0.343 m. Wavelength is spatial; period is temporal. Doubling frequency halves both the period and the wavelength (in the same medium).