Photon Energy CalculatorE = hf = hc ÷ λ
A photon’s energy is Planck’s constant times its frequency: E = hf = hc ÷ λ. A green 500 nm photon carries 3.97 × 10⁻¹⁹ J, or 2.48 eV, and a handy shortcut is E(eV) ≈ 1239.84 ÷ λ(nm). Enter a wavelength, frequency or energy to convert between them, see where the light sits on the electromagnetic spectrum, and count how many photons per second a laser or LED of a given power emits.
Formula verified against OpenStax — University Physics, Volume 3 · NIST — CODATA 2022 Fundamental Physical Constants
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Light source
h = 6.62607015 × 10⁻³⁴ J·s and c are exact SI constants.
Step-by-step working
What is photon energy?
Photon energy is the energy carried by a single particle of light, set entirely by its frequency or wavelength. Higher-frequency, shorter-wavelength light carries more energy per photon.
Max Planck introduced the idea in 1900 and Einstein used it to explain the photoelectric effect in 1905. Photon energy explains why UV causes sunburn, how solar cells and LEDs work, and why X-rays pass through soft tissue.
Quick answers
How do you calculate photon energy from wavelength?
E = hc ÷ λ. In handy units, E (eV) = 1239.84 ÷ λ (nm): a 620 nm red photon is 2.0 eV, and a 310 nm UV photon is 4.0 eV.
How many photons does a laser emit?
N = P ÷ E = Pλ ÷ hc. A 5 mW, 532 nm green laser pointer emits about 1.34 × 10¹⁶ photons per second.
What is an electronvolt?
The energy an electron gains crossing 1 volt: 1 eV = 1.602176634 × 10⁻¹⁹ J. Visible photons carry roughly 1.6–3.3 eV.
Why is UV light harmful when red light isn’t?
Each UV photon carries over 3.3 eV, enough to break chemical bonds in DNA. Red photons (≈ 1.9 eV) can’t, however many there are. Check any wavelength’s band above, or convert it with the frequency calculator.
Photon energy formula
h = 6.62607015 × 10⁻³⁴ J·s, c = 299,792,458 m/s and e = 1.602176634 × 10⁻¹⁹ C are all exact in the 2019 SI.
| Symbol | Meaning | SI unit |
|---|---|---|
| E | Photon energy | J or eV |
| h | Planck constant | J·s |
| f | Frequency | Hz |
| λ | Wavelength | m |
| c | Speed of light | m/s |
| N | Photons per second | 1/s |
How to calculate the energy of a photon
- Convert the wavelength to metres (500 nm = 5 × 10⁻⁷ m).
- Multiply h by c: 1.98645 × 10⁻²⁵ J·m.
- Divide by the wavelength to get joules.
- Divide by 1.602 × 10⁻¹⁹ to convert to electronvolts.
Worked example: a 500 nm green photon
What is the energy of a photon of green light at 500 nm?
E = 3.973 × 10⁻¹⁹ J = 2.480 eV (239.3 kJ per mole of photons)
A 1 mW red laser at 650 nm emits about 3.27 × 10¹⁵ photons every second.
Photon energies across the spectrum
| Radiation | Typical wavelength | Photon energy |
|---|---|---|
| Radio (FM) | 3 m | 4.1 × 10⁻⁷ eV |
| Microwave (Wi-Fi) | 12.5 cm | 1.0 × 10⁻⁵ eV |
| Infrared | 10 µm | 0.12 eV |
| Red light | 650 nm | 1.91 eV |
| Violet light | 400 nm | 3.10 eV |
| UV-C | 254 nm | 4.88 eV |
| Medical X-ray | 0.02 nm | ≈ 60 keV |
Common mistakes to avoid
- Leaving λ in nanometres in E = hc ÷ λ. It must be in metres, or use the 1239.84 ÷ nm shortcut for eV.
- Thinking brighter light has higher-energy photons. Brightness is the number of photons; colour sets the energy of each.
- Confusing eV and J. 1 eV = 1.602 × 10⁻¹⁹ J.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who became a full-time tech geek, and I’ve spent 13+ years designing and coding web tools. Photon energy comes up constantly in pharmaceutical analysis: UV-visible spectrophotometry, which identifies and assays drugs, is built on exactly this E = hc ÷ λ relationship.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Photon Energy Calculator: frequently asked questions
E = hf = hc ÷ λ, where h is Planck’s constant, f the frequency, c the speed of light and λ the wavelength.
Divide 1239.84 by the wavelength in nanometres.
No. Photons have zero rest mass, but they carry energy E = hf and momentum p = h ÷ λ.
h = 6.62607015 × 10⁻³⁴ J·s, exact since the 2019 SI redefinition. It links a photon’s energy to its frequency.
Gamma rays, with wavelengths shorter than about 0.01 nm and energies above roughly 100 keV.
References & sources
- OpenStax — University Physics, Volume 3 — Ch. 6.2, Photoelectric Effect and photon energy
- NIST — CODATA 2022 Fundamental Physical Constants — h, c and e (exact values)
- NASA Science — The Electromagnetic Spectrum — spectrum bands
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.