Energy to Wavelength Calculator
Enter a photon energy (in electronvolts, joules, or another unit) and this calculator returns the corresponding wavelength and frequency, the spectrum region, and the colour if it falls in the visible band. You can also start from a wavelength or frequency and solve for energy. Switch units freely - results update instantly, and the "Show your work" panel walks through every step of the calculation.
The energy-wavelength formula for photons
A photon carries a discrete packet of energy determined by two fundamental constants: Planck's constant h = 6.626×10^-34 J·s and the speed of light c = 2.998×10^8 m/s. The relationship is E = h·c / λ, where E is the photon energy and λ is its wavelength. Rearranging, λ = h·c / E, which is the formula this calculator applies. Because h·c equals approximately 1239.84 eV·nm, a convenient shortcut for visible-light calculations is E (eV) = 1239.84 / λ (nm). For example, green light at 500 nm has a photon energy of 1239.84 / 500 = 2.48 eV. Frequency follows from f = c / λ, so all three quantities are linked: know any one of them and you can find the other two.
How to use the four calculation modes
This calculator solves four related problems. "Wavelength from energy" takes a photon energy and returns the wavelength and frequency. "Energy from wavelength" reverses that: enter a wavelength and get the photon energy. "Wavelength from frequency" applies λ = c / f, which works for any electromagnetic wave even without invoking photon energy. "Frequency from wavelength" does the inverse. Each mode exposes only the inputs it needs, and all four output the spectrum region automatically. You can freely change energy units (eV, J, kJ, mJ, µJ, calorie), wavelength units (nm, µm, mm, m, angstrom, pm), and frequency units (Hz through THz) to match whatever values you have at hand.
Spectrum regions and why they matter
The electromagnetic spectrum is conventionally divided into regions by wavelength or photon energy. Radio and microwave photons carry very little energy (micro- to milli-electronvolts) and pass through most materials harmlessly. Infrared radiation is experienced as heat. Visible light - the narrow band from roughly 380 nm (violet) to 750 nm (red) - is what the human eye detects. Ultraviolet photons above about 3.1 eV carry enough energy to break chemical bonds, causing sunburn and, at shorter wavelengths, DNA damage. X-ray and gamma-ray photons are ionising: they can knock electrons off atoms, which is why medical X-rays require shielding and dosimetry. The energy-wavelength relationship makes all of this quantitative: the calculator tells you not just the wavelength but which region it belongs to and, for visible photons, what colour it appears.
Physical constants and precision
This calculator uses the CODATA 2018 exact values: h = 6.62607015×10^-34 J·s and c = 299,792,458 m/s (exact by definition). The compound constant h·c = 1239.841984 eV·nm is derived from these. Four significant figures are retained in displayed results; the underlying computation carries full IEEE 754 double-precision (about 15-16 digits). The speed of light value used is the exact SI-defined value in vacuum - propagation in any material is slower by a factor of the refractive index, which is not accounted for here.
Photon energy and wavelength across the EM spectrum
| Region | Typical wavelength | Photon energy (eV) | Notes |
|---|---|---|---|
| Gamma ray | < 10 pm | > 100 keV | Ionising; nuclear decay |
| X-ray | 10 pm - 10 nm | 124 eV - 124 keV | Ionising; medical imaging |
| Vacuum UV | 10 - 200 nm | 6.2 - 124 eV | Ionising; absorbed by air |
| UV-C (germicidal) | 200 - 280 nm | 4.4 - 6.2 eV | Kills bacteria and viruses |
| UV-B | 280 - 315 nm | 3.9 - 4.4 eV | Causes sunburn |
| UV-A | 315 - 400 nm | 3.1 - 3.9 eV | Tanning; some eye risk |
| Visible - violet | 380 - 450 nm | 2.76 - 3.26 eV | Human eye detects ~380-750 nm |
| Visible - blue | 450 - 495 nm | 2.51 - 2.76 eV | |
| Visible - green | 495 - 570 nm | 2.18 - 2.51 eV | Peak human eye sensitivity |
| Visible - yellow | 570 - 590 nm | 2.10 - 2.18 eV | |
| Visible - orange | 590 - 625 nm | 1.98 - 2.10 eV | |
| Visible - red | 625 - 750 nm | 1.65 - 1.98 eV | |
| Near-IR | 750 nm - 2.5 µm | 0.50 - 1.65 eV | Night-vision cameras |
| Mid-IR | 2.5 - 25 µm | 0.050 - 0.50 eV | Thermal imaging |
| Far-IR / THz | 25 µm - 1 mm | 1.2 - 50 meV | Security scanners |
| Microwave | 1 mm - 10 cm | 12 µeV - 1.2 meV | WiFi, radar, microwave ovens |
| Radio | > 10 cm | < 12 µeV | AM/FM, mobile, broadcast |
Representative photon energies and wavelengths for key EM spectrum regions. All conversions use h = 6.626×10^-34 J·s and c = 2.998×10^8 m/s.
Frequently asked questions
What is the formula for energy to wavelength?
The formula is λ = h·c / E, where λ is the wavelength in metres, h is Planck's constant (6.626×10^-34 J·s), c is the speed of light (3×10^8 m/s), and E is the photon energy in joules. In practical units, E (eV) = 1239.84 / λ (nm), which is handy for visible and near-UV calculations without the need for scientific notation.
What is an electronvolt (eV) and why use it instead of joules?
An electronvolt is the kinetic energy gained by a single electron when it accelerates through a potential difference of one volt: 1 eV = 1.602×10^-19 J. Because single-photon energies in joules are on the order of 10^-19 to 10^-34 (unwieldy numbers), eV gives human-scale values: visible photons range from about 1.65 eV (red) to 3.26 eV (violet). X-rays are measured in kiloelectronvolts (keV) and gamma rays in mega-electronvolts (MeV).
Does this formula apply to all electromagnetic waves or just visible light?
It applies to all photons across the entire electromagnetic spectrum, from radio waves to gamma rays. The formula E = h·c / λ holds regardless of region. The photon energy differs enormously - a 1 m radio-wave photon carries about 1.24 µeV while a 1 pm gamma-ray photon carries about 1.24 MeV - but the same formula connects them.
How do I convert wavelength to frequency?
Use f = c / λ, where c = 299,792,458 m/s and λ is in metres. For example, a 500 nm photon has a frequency of 2.998×10^8 / 5×10^-7 = 5.996×10^14 Hz, or about 600 THz. Select "Frequency from wavelength" in the mode selector above to do this instantly.
What wavelength does a 2.5 eV photon correspond to?
Using the shortcut formula: λ = 1239.84 / 2.5 = 495.9 nm, which is blue-green visible light, near the boundary of blue and green in the visible spectrum. This is the default example in the calculator.
Why does energy increase as wavelength decreases?
Because E = h·c / λ: energy is inversely proportional to wavelength. Shorter wavelengths (higher frequency) mean the wave oscillates more rapidly, and each cycle delivers more energy. Gamma rays with wavelengths of picometres are millions of times more energetic per photon than radio waves with wavelengths of metres.
Can I use this calculator for matter waves, not just light?
For photons (and other massless particles), E = h·c / λ is exact. For massive particles (electrons, neutrons), the de Broglie relation gives wavelength as λ = h / p, where p is momentum, and the kinetic energy relation is different. Use this calculator for electromagnetic radiation; for matter-wave problems you need the relativistic or non-relativistic kinetic energy formula instead.