How to use it
- Choose the value you know in Known quantity, then type it in the box that appears: Wavelength or Frequency.
- Type a wavelength with its prefix, for example 500 nm, or a frequency in hertz, for example 6.0e14 Hz.
- Read Frequency and Wavelength, then the Energy of one photon in joules and in electronvolts.
- Open How it is worked out to see c = λν and E = hν with the numbers.
The equations
Light and other electromagnetic waves have a wavelength λ and a frequency ν, and their speed c is the product of the two: c = λν. Because c is fixed, a longer wavelength means a lower frequency. The energy of a photon is E = hν, where h is Planck's constant; the same energy can be written E = hc/λ.
c = λ × ν = 299 792 458 m/s (exact)
ν = c ÷ λ
E = h × ν, with h = 6.626 070 15 × 10⁻³⁴ J/Hz (exact)
1 eV = 1.602 176 634 × 10⁻¹⁹ J (exact)- The three constants are exact in the SI system, so the only uncertainty in the result is in the numbers you type.
- Energy is proportional to frequency, so a photon of double the frequency has double the energy.
What the calculator does not cover
- Light in a medium. Light slows in water or glass, so its wavelength is shorter there at the same frequency. The calculator uses the speed in a vacuum and does not correct for that.
- Sound. Its waves travel at a speed set by the medium, not by c. For sound, use the Doppler effect calculator.
Worked example: light at 500 nm
A wavelength of 500 nm is 5.00 × 10⁻⁷ m. The frequency is f = c ÷ λ = 2.998 × 10⁸ m/s ÷ 5.00 × 10⁻⁷ m = 5.996 × 10¹⁴ Hz. One photon then has E = h × f = 6.626 × 10⁻³⁴ J·s × 5.996 × 10¹⁴ Hz = 3.973 × 10⁻¹⁹ J, which is 2.48 eV.
| Quantity | Value |
|---|---|
| Frequency | 5.996 × 10¹⁴ Hz |
| Energy of one photon | 3.973 × 10⁻¹⁹ J |
| Energy in electronvolts | 2.48 eV |
Frequently asked questions
How do I convert a wavelength to a frequency?
Divide the speed of light, 299 792 458 m/s, by the wavelength in metres. For 500 nm, which is 5.00 × 10⁻⁷ m, the frequency is 5.996 × 10¹⁴ Hz.
Why is the photon energy given in electronvolts?
An electronvolt is a convenient unit for the energy of one photon. Visible light gives a few electronvolts, where joules would be about 10⁻¹⁹. One electronvolt is exactly 1.602 176 634 × 10⁻¹⁹ J.
Why does a radio photon carry so little energy?
The energy of a photon is proportional to its frequency, and radio waves have much lower frequencies than visible light. A radio wave at 100 MHz has photons of about 4 × 10⁻⁷ eV, which is 413.6 neV.
Which prefixes can I type for the frequency?
Use k for thousands, M for millions and G for billions, such as 100 MHz. For terahertz, which the page does not read as a prefix, write the number with e notation, so 400 THz is 4.0e14 Hz.
Does the speed of light change in water or glass?
Yes, light slows in a medium such as water or glass, so its wavelength is shorter at the same frequency. This calculator uses the speed of light in a vacuum, and it does not correct for a medium.
Sources
- OpenStax Chemistry 2e, section 6.1: Electromagnetic Energy (c = λν, E = hν, E = hc/λ)
- NIST CODATA 2022: speed of light in vacuum c = 299 792 458 m/s (exact)
- NIST CODATA 2022: Planck constant h = 6.626 070 15 × 10⁻³⁴ J/Hz (exact)
- NIST CODATA 2022: elementary charge e = 1.602 176 634 × 10⁻¹⁹ C (exact), which gives the electronvolt
Figures and text last checked on Thursday, November 12, 2026.