Wavelength to Frequency Calculator (c = fλ and Photon Energy)
Choose what you know, enter a frequency or a wavelength, and optionally the refractive index of the medium. You get the other quantity, the wave speed and the energy of one photon.
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Formula
- Wave speed in a medium:
v = c ÷ n, withc = 299 792 458 m/sand refractive indexn(n = 1 in vacuum). - Wave relation:
v = f × λ, sof = c ÷ (n × λ)andλ = c ÷ (n × f). - Photon energy:
E = h × f, withh = 6.62607015e-34 J·s. - Electronvolts:
E(eV) = E(J) ÷ 1.602176634e-19.
The frequency does not change when a wave enters another medium; the speed and the wavelength do.
Worked example
A green laser has a vacuum wavelength of 532 nm.
f = 299 792 458 ÷ 532e-9 = 5.63520e14 HzE = 6.62607015e-34 × 5.63520e14 = 3.73392e-19 JE = 3.73392e-19 ÷ 1.602176634e-19 = 2.33053 eV
Light of 500 nm inside glass with n = 1.5: f = 299 792 458 ÷ (1.5 × 500e-9) = 3.99723e14 Hz.
Reading the results
Realistic values are tiny or huge, so the wavelength is shown with a readable unit (m, mm, µm or nm) and also in scientific notation, and the photon energy is shown in scientific notation in joules and electronvolts. For 100 MHz that gives λ = 2.9979e+0 m, E = 6.6261e-26 J and E = 4.1357e-7 eV. Wavelength and frequency are computed to 10 significant digits.
Frequently asked questions
How do you convert wavelength to frequency?
Divide the wave speed by the wavelength: f = v ÷ λ. In vacuum v is the speed of light, 299,792,458 m/s. A 532 nm green laser has f = 299,792,458 ÷ 532e-9 = 5.635e14 Hz.
What changes when light enters glass or water?
The frequency stays the same, but the speed drops to c ÷ n and the wavelength shrinks by the same factor. 500 nm light in glass with n = 1.5 has a wavelength of 333 nm in the glass and a speed of about 199,861,639 m/s.
How is photon energy calculated?
E = h × f, with Planck's constant h = 6.62607015e-34 J·s. A 5.635e14 Hz photon has 3.734e-19 J. Dividing by 1.602176634e-19 J per electronvolt gives 2.33 eV.
Does the wavelength entered mean the wavelength in vacuum?
No. When you solve for frequency, the wavelength is taken to be the wavelength in the medium you chose with the refractive index. Catalogue wavelengths for lasers and spectral lines are usually vacuum values, so leave the index at 1 for those.
What is the wavelength of a 100 MHz FM radio signal?
In air, which is very close to vacuum for radio, λ = 299,792,458 ÷ 100,000,000 = 2.998 m, so about 3 metres.