Wavelength & Frequency Calculator

Electromagnetic radiation, light, radio waves, X-rays, microwaves, is a wave whose energy, frequency, and wavelength are linked by two universal relations:

c = λ · f and E = h · f

The first is the wave equation applied to light: the speed of light in vacuum (c = 299,792,458 m/s, an exact SI defining constant) equals the product of wavelength and frequency. The second is the Planck-Einstein relation: a single photon's energy is the Planck constant (h = 6.62607015 × 10⁻³⁴ J·s, also exact) times its frequency. Combining them gives E = h · c / λ, which lets you convert any one of the three quantities into the other two. This calculator does that conversion in the browser, in real time, with the exact defining constants and a clear spectrum-band readout for whatever wavelength you enter.

The same relations work for every part of the electromagnetic spectrum, from kilometre-long AM radio waves to femtometre-scale gamma rays emitted by atomic nuclei. The numerical values change by 14 orders of magnitude; the algebra does not.

How to use the calculator

1. Type into any field. Wavelength, frequency, or photon energy, the other two update automatically because all three are linked by the same algebra.
2. Choose the wavelength unit. Seven prefixes are supported: nm (nanometre, 10⁻⁹ m), μm (micrometre, 10⁻⁶ m), Å (ångström, 10⁻¹⁰ m), mm, cm, m, and km. Switching unit mid-calculation rescales the input value without losing precision.
3. Choose the frequency unit. Five prefixes are supported: Hz, kHz, MHz, GHz, and THz. The wavelength and frequency fields together cover the full spectrum from kHz radio to PHz gamma rays.
4. Read off the band indicator. Below the inputs a coloured chip shows which electromagnetic band the current wavelength falls into: radio, microwave, infrared, visible (with sub-band colour), ultraviolet, X-ray, or gamma.
5. Use the preset chips for quick checks. Five preset chips load common reference cases (500 nm green light, 1 m FM radio, 5 GHz Wi-Fi, 1 eV red/IR, 0.001 nm gamma ray). These exercise every conversion path.

The "Formulas & current values" panel below the inputs shows the live check that λ · f actually equals c, and that E/f equals h, in the displayed units.

The wave equation c = λ · f

For any periodic wave travelling at constant speed, the speed is the product of the wavelength (the distance between consecutive peaks) and the frequency (the number of peaks passing a fixed point per second). For electromagnetic radiation in vacuum, and to an excellent approximation in air, the speed is the universal constant c, exactly 299,792,458 m/s by the 1983 SI definition of the metre. Rearranged, the equation gives two practical formulas:

f = c / λ and λ = c / f

A 100 MHz FM radio wave has wavelength λ ≈ 2.998 m. A 500 nm green photon has frequency f ≈ 5.996 × 10¹⁴ Hz, or about 599.58 THz. Both answers are quick mental arithmetic once you have the constant memorized to four digits.

The relation holds in any transparent medium, but the speed drops. In glass of refractive index 1.5 the speed of light is c / 1.5 ≈ 2 × 10⁸ m/s, so a 500 nm photon inside glass would have wavelength ≈ 333 nm, shorter by the same factor. The frequency is unchanged across the boundary; only the wavelength (and the speed) shift.

The Planck-Einstein relation E = h · f

In 1900 Max Planck showed that the energy of a light quantum is proportional to its frequency; Einstein made the proportionality explicit in 1905 to explain the photoelectric effect. The constant h = 6.62607015 × 10⁻³⁴ J·s has been an exact SI defining constant since the 2019 kilogram redefinition. The product h · c is itself a useful constant at 1.986 × 10⁻²⁵ J·m, often written ħc ≈ 197 MeV·fm in particle-physics contexts.

Photon energies are usually quoted in electron-volts (1 eV = 1.602176634 × 10⁻¹⁹ J), which is the unit this calculator uses by default. A 1 eV photon has frequency f ≈ 242 THz and wavelength λ ≈ 1240 nm, squarely in the near-infrared, just past the red edge of human vision. The band gap of silicon is 1.12 eV, which corresponds to a photon wavelength of about 1107 nm, that is why silicon solar cells respond to visible and near-IR light but not to longer-wavelength thermal IR.

Electromagnetic spectrum bands

The spectrum is divided into seven bands by convention. Boundaries vary slightly between textbooks, but the engineering practice is roughly: radio (λ > 1 mm, f < 300 GHz), microwave (1 mm-1 μm, 300 GHz-300 THz), infrared (1 μm-700 nm), visible (700 to 380 nm), ultraviolet (380 to 10 nm), X-ray (10 to 0.01 nm), and gamma (< 0.01 nm). The calculator's band indicator highlights the active band in real time, with the visible sub-band broken out into violet (380 to 450 nm), blue (450 to 485 nm), cyan (485 to 500 nm), green (500 to 565 nm), yellow (565 to 590 nm), orange (590 to 625 nm), and red (625 to 740 nm). The seven-colour convention dates to Newton's optics but is now standard in display engineering (sRGB uses roughly the same primaries).

Human colour perception is determined by three cone types in the retina, with peak sensitivities near 420 nm (S, "blue"), 534 nm (M, "green"), and 564 nm (L, "red"). Photon energy decreases as wavelength increases, a red photon at 700 nm carries about half the energy of a violet photon at 400 nm. That is why a single red laser pointer feels much less intense than a single violet laser pointer at the same output power, and why UV photons can break chemical bonds that visible photons of comparable brightness cannot.

Worked examples

Example 1: green light at 500 nm

f = c / λ = 299,792,458 / (500 × 10⁻⁹) ≈ 599.58 THz. E = h · f ≈ 2.480 eV. The calculator classifies this in the visible green sub-band.

Example 2: FM radio at 100 MHz

λ = c / f = 299,792,458 / 100,000,000 ≈ 2.998 m. Photon energy E ≈ 4.14 × 10⁻⁷ eV, vanishingly small compared to thermal energy at room temperature (kT ≈ 25.7 meV), which is why radio photons do not ionise atoms or drive chemistry.

Example 3: Wi-Fi at 5 GHz

λ = c / f ≈ 59.96 mm. The router's printed-circuit patch antenna is typically a quarter-wave, or about 1.5 cm. Photon energy at 5 GHz is about 20.7 μeV, well below thermal noise.

Example 4: 1 eV photon (red edge of visible)

f = E / h ≈ 241.83 THz, λ ≈ 1240 nm. That wavelength falls in the near-infrared band, just past the long-wavelength end of human vision. Silicon photodiodes respond up to about 1100 nm, so a 1240 nm photon is below their band gap.

Example 5: gamma ray at 0.001 nm

f = c / λ ≈ 2.998 × 10²⁰ Hz ≈ 300 EHz. E ≈ 1.24 MeV. This is the regime of nuclear gamma decay: a Co-60 source emits two gamma photons at 1.17 and 1.33 MeV during nickel-60 decay. Such photons are ionising radiation and require heavy shielding (centimetres of lead, or metres of concrete).

Where this calculation shows up

Wireless engineering. Antenna design begins with λ/2 or λ/4 element lengths. A 2.4 GHz Wi-Fi antenna is ~31 mm; a 5G mm-wave antenna at 28 GHz is ~2.7 mm. Every printed-circuit patch, dish, and phased array is sized in fractions of a wavelength.

Photonics and lasers. Laser safety classifications depend on wavelength (because eye-damage thresholds vary across the spectrum) and on power or energy per pulse. A 1064 nm Nd:YAG laser at moderate power is "Class 4" because the eye cannot blink fast enough to avoid retinal damage even though the photon is invisible.

Spectroscopy. UV-Vis absorbance spectra report absorbance vs wavelength; IR spectra report transmittance vs wavenumber (cm⁻¹, the reciprocal of wavelength in centimetres). Converting between wavenumber, frequency, and wavelength uses the same c constant.

Astronomy. Redshift z = (λ_observed − λ_emitted) / λ_emitted is reported as a dimensionless number or as a frequency shift. A galaxy with z = 1 has its 500 nm light shifted to 1000 nm, which is the near-IR.

Medical imaging. X-ray tubes operate at photon energies of 30 to 150 keV (wavelengths of 0.04 to 0.008 nm). CT scanners and mammography units use the same physics with different energies for different tissue contrasts.

Common mistakes

• Confusing electron-volts with joules. 1 eV = 1.602 × 10⁻¹⁹ J. Photon energies are reported in eV by convention in atomic and solid-state physics, but joules are the SI unit.
• Mixing up wavenumber and wavelength. IR spectroscopists quote wavenumber in cm⁻¹, which is the reciprocal of wavelength in centimetres. A 1500 cm⁻¹ band corresponds to λ = 6.67 μm.
• Forgetting that frequency is conserved across a boundary. When light enters glass, its wavelength shortens by 1/n but its frequency stays the same. The energy E = h·f is therefore also unchanged.
• Using the speed of light in a medium. Inside a transparent material with refractive index n, the speed is c / n. Use that reduced speed if you are computing λ inside the material, but use the source frequency (which is unchanged).

Frequently Asked Questions

What is the speed of light, and is it really exact? The speed of light in vacuum is exactly 299,792,458 m/s by the 1983 SI definition of the metre. The metre is now defined as the distance light travels in 1/299,792,458 of a second. The number is exact; no measurement uncertainty.

What is the Planck constant, and why does it matter here? The Planck constant h = 6.62607015 × 10⁻³⁴ J·s is an exact defining constant since the 2019 SI redefinition. It converts between the frequency of a photon and its energy via E = h · f. Combined with c, it lets you derive any of the three EM variables from any other.

Why is photon energy reported in electron-volts? The electron-volt is the kinetic energy gained by an electron crossing a 1-volt potential. It equals exactly 1.602176634 × 10⁻¹⁹ J. Atomic, molecular, and solid-state physics deal in electron-volts because chemical bond energies, band gaps, and ionisation energies all sit conveniently between 1 and 10 eV.

What are the seven electromagnetic spectrum bands? By convention: radio (λ > 1 mm), microwave (1 mm-1 μm), infrared (1 μm-700 nm), visible (700 to 380 nm), ultraviolet (380 to 10 nm), X-ray (10 nm-0.01 nm), and gamma (< 0.01 nm). Boundaries are approximate and overlap between disciplines.

What colour is a 500 nm photon? 500 nm falls in the visible green sub-band (500 to 565 nm). Human colour perception peaks in sensitivity near 555 nm under photopic lighting.

What is the wavelength range of Wi-Fi? Wi-Fi operates in the 2.4 GHz and 5 GHz microwave bands. At 2.4 GHz, λ ≈ 12.5 cm. At 5 GHz, λ ≈ 6 cm. At 6 GHz (Wi-Fi 6E), λ ≈ 5 cm. All are well inside the microwave band.

Can I use this calculator for sound waves? No, this calculator uses c = 299,792,458 m/s, the speed of electromagnetic waves in vacuum. Sound in air travels at about 343 m/s, three orders of magnitude slower. Use a separate wave-speed calculator for acoustic problems.

What is the photon energy of a 1 MHz radio wave? E = h · f ≈ 4.14 × 10⁻⁹ eV (4.14 neV). This is fourteen orders of magnitude below thermal energy kT ≈ 25.7 meV at room temperature, which is why radio waves do not ionise or heat matter in the way infrared or visible photons do.

References

• NIST (2019). SI Base Units. https://www.nist.gov/si-base-units
• CODATA 2018. Internationally recommended values of the fundamental physical constants. https://physics.nist.gov/cuu/Constants/
• ISO 80000-7:2018. Quantities and units, Part 7: Light and radiation.
• Born, M., Wolf, E. (1999). Principles of Optics, 7th ed. Cambridge University Press.
• Hecht, E. (2017). Optics, 5th ed. Pearson.

More Tools

Explore our physics-momentum calculator for a related energy-and-velocity problem, or try the Ohm's Law Calculator if your work involves AC circuits at radio frequencies.

Disclaimer

This calculator is provided for general educational and utility purposes. Verify electromagnetic-spectrum assumptions, refractive indices, and unit conventions against the specification of the system or experiment you are working with.

Worked Examples and Edge Cases

The examples below cover cases that frequently trip up a first-time user: unit mismatches, frequency-vs-wavelength consistency at material boundaries, sub-band boundaries, and the relationship between colour and dominant wavelength.

Example 6: round-trip check. Enter λ = 500 nm; the frequency field updates to 599.58 THz and the energy field to 2.480 eV. Now type 599.584916 into the frequency field (THz). The wavelength field should return to 500.000 nm within the display precision, and λ · f should equal c = 299,792,458 m/s exactly.

Example 7: typing energy first. A common workflow is to know a photon's energy from a spectroscopic measurement and want to know the wavelength and frequency. Type 1.240 eV into the energy field. The wavelength field shows 1000.0 nm and the frequency field shows 299.79 THz. This corresponds to the silicon band edge (1.12 eV ≈ 1107 nm) almost exactly.

Example 8: very long radio waves. Enter 1000 m as the wavelength. The frequency is 299.79 kHz, in the LF (low-frequency) broadcast band. The energy field shows 1.24 × 10⁻⁹ eV. The band indicator shows "Radio".

Example 9: very short gamma rays. Enter 0.0001 nm. The frequency is 2.998 × 10²¹ Hz (about 3 ZHz), and the energy is 12.4 MeV. This is in the gamma band. Typical medical linacs produce 6 MV photons, which corresponds to λ ≈ 0.002 nm and E ≈ 12 MeV at the maximum-energy tip of the bremsstrahlung spectrum.

Example 10: edge of the visible band. Enter 700 nm; the indicator says "Visible" with sub-band "red". Enter 380 nm; the indicator remains "Visible" but the sub-band changes to "violet". Cross these boundary values carefully, some textbooks cite 380 nm and others 400 nm as the violet edge, and 700 nm vs 750 nm as the red edge. The calculator uses 380 to 740 nm for the visible range.

Example 11: Ångström unit for spectroscopy. Spectroscopists often quote wavelengths in Ångströms (1 Å = 0.1 nm). Set the wavelength unit to Å and type 5000, the field shows 5000 Å and the underlying value is 500 nm (green light). The frequency and energy fields do not change because Å is just a rescaling of the same physical wavelength.

Example 12: changing wavelength unit mid-calculation. Enter 500 nm. Switch the unit dropdown from nm to μm. The displayed value updates to 0.5, and the underlying frequency and energy fields do not change (they were already computed from the canonical 500 nm). The convenience is that you can read the result in your preferred unit without retyping.

Practical Tips

• Memorize c to four digits. 3 × 10⁸ m/s is a useful approximation; 299,792,458 m/s is the exact value. Mental arithmetic for radio engineering benefits from keeping 300 × 10⁶ m/s at hand.
• Memorize h · c. The product 1.986 × 10⁻²⁵ J·m divided by 1.602 × 10⁻¹⁹ J/eV gives ≈ 1240 eV·nm. The rule of thumb "1240 / λ(nm) = E(eV)" is exact to 0.1% and lets you estimate photon energies without the calculator.
• Always quote units. A "wavelength" without a unit is meaningless, the same number can be nanometres, ångströms, or millimetres.
• Cross-check with two fields. Type the measured frequency into the frequency field and check that the wavelength field returns your original value. Round-trip checks catch typos and unit mismatches.
• Remember that refractive index shifts wavelength, not frequency. Inside glass, λ is shorter than in air, but f is unchanged.

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