Light, radio waves, X-rays and gamma rays are all electromagnetic radiation — the only difference between them is their wavelength (and therefore frequency and energy). This calculator lets you convert freely between all three quantities in any direction, across the full span of the EM spectrum, using the exact SI-defined constants.
The three fundamental relationships
Three equations tie wavelength, frequency and photon energy together:
c = f · λ — the wave equation for light in vacuum
E = h · f — Planck’s relation for photon energy
E = h · c ÷ λ — combining both (useful when you know λ and want E directly)
The constants are:
| Symbol | Value | Name |
|---|---|---|
| c | 2.99792458 × 10⁸ m/s | Speed of light in vacuum (exact) |
| h | 6.62607015 × 10⁻³⁴ J·s | Planck constant (exact, 2019 SI) |
| 1 eV | 1.602176634 × 10⁻¹⁹ J | Electron-volt (exact) |
Both c and h have been exact by definition since the 2019 redefinition of the SI base units, so results carry no rounding uncertainty from the constants themselves — only from your input value.
How the calculator works
Select which quantity you know, enter the value and unit, and the calculator derives the other two. All three modes are internally equivalent:
- From wavelength: applies f = c ÷ λ, then E = h · f
- From frequency: applies λ = c ÷ f, then E = h · f
- From energy: applies f = E ÷ h, then λ = c ÷ f
Output units are independently selectable, so a radio engineer can read frequency in MHz while simultaneously reading wavelength in metres, without any mental arithmetic.
The EM spectrum band badge auto-classifies the result: gamma, X-ray, ultraviolet, visible, infrared, microwave or radio. For wavelengths in the visible range (380–750 nm) the badge also shows the approximate perceived colour, from violet through red.
Worked example: green laser pointer
A green laser pointer emits at 532 nm (a common doubled-YAG wavelength):
- Set “solve for frequency and energy from wavelength”
- Enter 532, unit nm
- Read out:
- Frequency: 5.636 × 10¹⁴ Hz ≈ 563.6 THz
- Energy: 3.735 × 10⁻¹⁹ J ≈ 2.33 eV
- Band: Visible (yellow-green)
Changing the output wavelength unit to Å (ångströms) gives 5320 Å — the unit still widely used in spectroscopy and crystallography.
Worked example: Wi-Fi 2.4 GHz
Set “solve for wavelength and energy from frequency”, enter 2.4, unit GHz:
- Wavelength: 0.1249 m ≈ 12.5 cm
- Energy: 9.937 × 10⁻²⁴ J ≈ 62.0 µeV
- Band: Microwave
The 12.5 cm wavelength is why a microwave oven cavity and a Wi-Fi router are similar in physical size — they share the same frequency band.
Worked example: medical X-ray
A diagnostic X-ray machine typically uses photons around 100 keV. Set “solve for wavelength and frequency from energy”, enter 100, unit keV:
- Frequency: 2.418 × 10¹⁹ Hz (24.18 EHz)
- Wavelength: 1.240 × 10⁻¹¹ m ≈ 12.4 pm ≈ 0.124 Å
- Band: X-rays
The wavelength is comparable to the spacing between atoms in a crystal lattice (~100–300 pm), which is why X-ray crystallography can resolve atomic structure.
Unit guide
| Unit | Meaning | Typical use |
|---|---|---|
| nm | nanometre (10⁻⁹ m) | Visible / UV / near-IR optics |
| µm | micrometre (10⁻⁶ m) | Thermal IR, fibre optics |
| Å | ångström (10⁻¹⁰ m) | Spectroscopy, crystallography |
| pm | picometre (10⁻¹² m) | Hard X-rays, gamma rays |
| THz | terahertz (10¹² Hz) | Optics, spectroscopy |
| GHz | gigahertz (10⁹ Hz) | Radar, Wi-Fi, satellite |
| eV | electron-volt | Atomic / molecular transitions |
| keV | kilo–electron-volt | X-ray, medical imaging |
| MeV | mega–electron-volt | Nuclear physics, particle beams |
All calculations run entirely in your browser — no values are sent to any server.