How this calculator works
- Step 1WavelengthλDistance between crests.
- Step 2Frequencyν = c ÷ λCrests passing each second.
- Step 3EnergyE = h νCarried by each photon.
Light and all electromagnetic waves travel at the same speed in a vacuum, c. So wavelength and frequency are locked together: longer waves have lower frequency.
Each photon carries energy proportional to its frequency, E = hν. Short-wavelength light, like ultraviolet, carries more energy per photon than red light.
Worked example: OpenStax Example 6.1
- ν
c ÷ λ
- Wavelength589 × 10⁻⁹ m5.89 × 10⁻⁷ m
- Frequency299,792,458 ÷ 5.89 × 10⁻⁷5.090 × 10¹⁴ Hz
- Photon energyh × ν3.373 × 10⁻¹⁹ J
OpenStax, using c = 2.998 × 10⁸ m/s, gives 5.09 × 10¹⁴ s⁻¹.
Read the result
- 640 nm red light3.104 × 10⁻¹⁹ JPer photon: 1.9373 eV (OpenStax Example 6.2).
- 2.45 GHz microwave12.2364 cmPer photon only 1.623 × 10⁻²⁴ J.
An 850 MHz radio wave is 35.2697 cm long: radio and light are the same kind of wave at very different frequencies.
Assumptions and limits
- VacuumIn air the speed is 0.03% lower.
- Exact constantsc, h and e are fixed SI values.
- Not in glassIn water or glass, wavelength shrinks.
- Per photonTotal energy depends on how many photons.
Related science tools
Wavelength and frequency multiply to the wave's speed.
For very large or small values, the scientific notation calculator writes them as a × 10ⁿ. Sound levels are handled by the decibel calculator.
Common mistakes
Mistake: Using nm directly in c = λν.
Instead: Convert nm to metres; the tool does it.
Mistake: Thinking brighter light has more energy per photon.
Instead: Brighter means more photons; colour sets energy per photon.
Checking the method
A separate script works through the photon energy in exact fractions and reproduces OpenStax Examples 6.1 and 6.2 and the 850 MHz check.
Read how we test our calculators, or browse more maths calculators.