Photon Energy Calculator
Calculate photon energy from wavelength using E = hc / lambda, with the result given in both joules and electronvolts.
Photon Energy Calculator
Calculator
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Formula: E = hf = hc/λ
Worked example — 2.25 eV
Formula
E = hf = hc/λ
Energy of a photon. h = 6.626×10⁻³⁴ J·s, c = 2.998×10⁸ m/s.
Worked Examples
Example 1: Green light
Problem:λ=550nm
Solution:E=6.626e-34×3e8/550e-9=3.61e-19 J=2.25 eV
Result:2.25 eV
Frequently Asked Questions
What is photon energy and how is it calculated?
A photon's energy is given by E = hf = hc/λ, where h = 6.626×10⁻³⁴ J·s (Planck's constant), c = 2.998×10⁸ m/s (speed of light), and λ is the wavelength. Shorter wavelengths produce higher-energy photons.
How do you convert photon energy between joules and electron-volts?
1 electron-volt (eV) = 1.602×10⁻¹⁹ J. To convert: eV = E(J) / 1.602×10⁻¹⁹. Visible light photons range from about 1.8 eV (red, 700 nm) to 3.1 eV (violet, 400 nm). X-ray photons exceed 100 eV.
What units are used in photon energy calculations?
Wavelength λ is entered in nanometres (nm). Energy is output in both joules (J) and electron-volts (eV). Frequency f is in terahertz (THz = 10¹² Hz). Planck's constant h = 6.626×10⁻³⁴ J·s and c = 2.998×10⁸ m/s are used internally.
What is the photoelectric effect and why does photon energy matter?
In the photoelectric effect, a photon must have energy above the material's work function to eject an electron. For example, zinc has a work function of ~4.3 eV, so UV photons (λ < 290 nm) are needed. This principle underpins solar cells and photodetectors.
How are wavelength, frequency and photon energy connected?
Because c = f x lambda, the two forms E = h x f and E = h x c / lambda describe the same quantity. Energy is inversely proportional to wavelength, so halving the wavelength doubles the photon energy. A shortcut worth memorising is that h x c is about 1240 eV nm, so E(eV) = 1240 / lambda(nm). Green light at 550 nm therefore carries 1240/550 = 2.25 eV, matching the calculator.
Why can ultraviolet light damage molecules when radio waves cannot?
Chemical bonds typically require a few electron-volts to break, and photons act one at a time. A 300 nm ultraviolet photon carries 1240/300 = 4.1 eV, easily enough to disrupt bonds in DNA. A 100 MHz radio photon carries h x f = 6.6 x 10^-26 J, about 4 x 10^-7 eV - millions of times too little. Turning up the intensity supplies more photons, never more energy per photon.
How do you find how many photons a light beam delivers per second?
Divide the optical power by the energy of a single photon: n = P / E. A 1 mW laser at 532 nm emits photons of 1240/532 = 2.33 eV, which is 2.33 x 1.602 x 10^-19 = 3.73 x 10^-19 J each. So n = 10^-3 / 3.73 x 10^-19 = 2.7 x 10^15 photons per second. The huge count is why ordinary light sources look continuous rather than granular.
What is the difference between photon energy and light intensity?
Photon energy is fixed by wavelength alone; intensity counts how many photons arrive per second per unit area. The distinction is what made the photoelectric effect so decisive: shining an intense beam of below-threshold light on a metal ejects no electrons at all, however bright it is, while a single photon above the work function does the job immediately. Energy is quantised per photon, not spread across the beam.
How do photon energies map onto the electromagnetic spectrum?
Using E(eV) = 1240/lambda(nm): visible light from 700 nm to 400 nm spans about 1.77 to 3.1 eV; ultraviolet from 400 nm down to 315 nm runs about 3.1 to 3.9 eV and climbs from there; infrared beyond 700 nm falls below 1.77 eV. X-rays with sub-nanometre wavelengths reach the kiloelectron-volt range, which is why they penetrate tissue and can ionise atoms.
Why does photon energy matter for solar cells and LEDs?
A semiconductor only absorbs photons whose energy exceeds its bandgap; lower-energy photons pass straight through. Silicon's bandgap of roughly 1.1 eV corresponds to about 1100 nm, setting the long-wavelength limit of a silicon cell, while any energy above the gap is wasted as heat. LEDs run the process in reverse and emit near their bandgap, so a blue LED emitting around 460 nm corresponds to roughly 2.7 eV.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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