Photon Energy Calculator
Compute the energy of a single photon from its wavelength using E = hc/λ, the Planck-Einstein relation. Returns energy in joules; convert to electron-volts by dividing by 1.602 × 10⁻¹⁹.
Last updated: May 2026
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About this calculator
The formula is E = hc/λ, where h = 6.626 × 10⁻³⁴ J·s is Planck's constant, c = 3 × 10⁸ m/s is the speed of light, and λ is the photon's wavelength in metres. The calculator uses these rounded values rather than CODATA exact values (h = 6.62607015e−34 exactly; c = 299,792,458 exactly), introducing small (~0.01%) errors that are negligible for most purposes but matter for precision spectroscopy. Photon energy scales inversely with wavelength: short wavelengths (high frequencies) have high energies; long wavelengths have low energies. Reference points: visible light (λ ≈ 400–700 nm) has photon energies of ~1.8–3.1 eV; UV-A (~315–400 nm) ~3.1–3.9 eV; UV-B/C (~100–315 nm) ~3.9–12 eV; X-rays (~0.01–10 nm) ~120 eV–120 keV; γ-rays (<0.01 nm) >120 keV; infrared (~700 nm–1 mm) <1.8 eV; microwaves (~1 mm–1 m) ~10⁻⁶–10⁻³ eV; radio waves (>1 m) very low. Edge cases: λ = 0 produces division by zero. Very small wavelengths (γ-rays) produce extremely high energies (MeV-range); very large wavelengths (radio) produce extremely low energies. The formula uses the photon's wavelength in vacuum; in a medium with refractive index n, c reduces to c/n but frequency stays constant, so E remains the same — the photon's energy is fixed by its source, not by the medium. Equivalent forms: E = hν (h times frequency), E = ℏω (reduced Planck constant times angular frequency).
How to use
Example 1 — green light photon. λ = 500 nm = 5 × 10⁻⁷ m. Step 1: hc = 6.626e−34 × 3e8 ≈ 1.988e−25 J·m. Step 2: E = 1.988e−25 / 5e−7 = 3.976e−19 J. Step 3: convert to eV: 3.976e−19 / 1.602e−19 ≈ 2.48 eV. Verify: green light photon energy is conventionally ~2.5 eV, matching ✓. This is enough to drive most photovoltaic reactions in silicon (1.1 eV bandgap), excite chlorophyll for photosynthesis, and trigger common photoreceptors in the human eye. Example 2 — X-ray photon. λ = 0.1 nm = 1 × 10⁻¹⁰ m (typical medical X-ray). Step 1: E = 1.988e−25 / 1e−10 = 1.988e−15 J. Step 2: convert to keV: 1.988e−15 / 1.602e−19 ≈ 12,400 eV ≈ 12.4 keV. Verify: medical-imaging X-rays use 10–150 keV photons, depending on tissue; 12.4 keV at 0.1 nm is consistent ✓. Photons of this energy easily ionise atoms and break chemical bonds, which is why X-ray exposure must be controlled. Memorise the conversion: 1240 eV·nm ÷ λ(nm) = E(eV) — useful for quick mental estimates.
Frequently asked questions
What's the difference between photon energy E = hν and E = hc/λ?
They are mathematically equivalent: ν (frequency) and λ (wavelength) are related by c = λν (in vacuum). Substituting ν = c/λ into E = hν gives E = hc/λ. Use whichever input you have: frequency-based instruments (radio, microwave) report ν; wavelength-based instruments (UV-vis spectroscopy) report λ. For photons in a medium with refractive index n, the speed becomes c_medium = c/n, the wavelength shortens (λ_medium = λ_vac/n), but the frequency stays the same — so ν and E are unchanged when light enters a different medium. This is why photon energy is well-defined regardless of the medium it propagates through. The angular-frequency form E = ℏω with ℏ = h/(2π) and ω = 2πν is preferred in quantum mechanics for cleaner equations, particularly when dealing with creation/annihilation operators of photons in quantum electrodynamics.
How does photon energy relate to colour, vision, and photochemistry?
Visible light spans roughly 400 nm (violet, ~3.1 eV) to 700 nm (red, ~1.8 eV). Wavelengths below 400 nm (UV) have enough energy to break weak chemical bonds and damage DNA, which is why UV-B and UV-C cause sunburn and skin cancer. Above 700 nm (infrared), photons are too weak to excite common electronic transitions and mainly cause vibrational/thermal effects. Photoreceptors in the human eye absorb specific wavelength ranges: rod cells (rhodopsin) peak around 500 nm; cone cells peak around 420 nm (blue), 530 nm (green), and 560 nm (red) — colour vision comes from the brain comparing relative responses. Photosynthesis uses photons of 400–700 nm (PAR, photosynthetically active radiation) absorbed by chlorophyll a (max ~430, 660 nm) and b (~460, 640 nm). For photolithography and laser eye surgery, the energetic UV photons selectively break bonds in target materials. Below ~1.1 eV, photons cannot generate electron-hole pairs in silicon solar cells, setting the minimum useful wavelength for photovoltaics.
Why is the eV unit so popular for photon energy?
1 eV (electron-volt) = 1.602 × 10⁻¹⁹ J — the energy gained by an electron accelerated through 1 volt. It's the natural energy scale for atomic and molecular processes: hydrogen's ionisation energy is 13.6 eV, typical chemical bonds are 1–5 eV, semiconductor bandgaps are 0.5–6 eV (silicon 1.1, GaAs 1.4, diamond 5.5), X-ray photons are 100 eV–100 keV, γ-ray photons are 100 keV–10+ MeV. The handy mental rule is E(eV) = 1240/λ(nm) — derived from hc ≈ 1240 eV·nm. So green light at 500 nm has 2.48 eV, blue at 450 nm has 2.76 eV, red at 700 nm has 1.77 eV. The conversion to joules (× 1.602e−19) is annoying enough that eV is preferred in most quantum-mechanics, condensed-matter, and atomic-physics literature. Particle physicists scale up to keV (10³), MeV (10⁶), GeV (10⁹), TeV (10¹²). For radio waves, the natural unit drops to μeV or smaller and joules become impractical.
What are the common mistakes when computing photon energy?
The biggest mistake is unit confusion in wavelength: 500 nm is 5e-7 m, not 500 m or 500e-9 cm. Always convert to m before plugging into E = hc/λ. The second is using rounded h and c (the calculator uses 6.626e-34 and 3e8, off by ~0.01% from CODATA exact values) for precision spectroscopy work; use h = 6.62607015e-34 and c = 299792458 for that. The third is mistaking photon energy for total beam energy or photon flux — the formula gives energy per single photon, not the energy of a laser pulse or a sunbeam. To get power or fluence, multiply by photon count per second or per area. People also confuse vacuum wavelength with wavelength in a medium; E is invariant, so use vacuum (or air, ≈ vacuum) wavelength. Inverting the formula incorrectly (using E·λ or E/λ instead of E = hc/λ) gives wrong magnitudes. Finally, the eV ↔ joule conversion is the most common slip: 1 eV = 1.602e-19 J, multiply (not divide) by this to go from eV to J.
When should I not use this calculator?
Do not use it for photons in a medium where the relevant wavelength is the in-medium one — use vacuum wavelength (frequency-defined) since E doesn't change with refractive index. It is not appropriate for matter waves of massive particles (electrons, neutrons) — those use λ = h/(mv), the de Broglie relation. Do not use it for bulk-beam energetics; the formula gives single-photon energy, and total beam energy requires multiplying by photon count. It is unsuitable for non-monochromatic light (lamps, sunlight) without integrating across the spectrum — quote either average photon energy weighted by intensity or the integrated energy density. The calculator's rounded h and c are accurate to ~0.01%; for higher precision (spectroscopy, atomic clocks), use the full CODATA values. For high-energy γ-ray or cosmic-ray photons where energy is more naturally specified than wavelength, invert: λ = hc/E. Finally, do not apply this formula to virtual photons (off-shell) in QED — they have E and p but don't satisfy E = pc and have no simple wavelength.