Convert wavelength to frequency and photon energy, or back, with c = fλ and E = hf, and see where the wave sits in the electromagnetic spectrum.
550 nm is visible light (green): it oscillates at 545.08 THz and each photon carries 2.25426 eV.
c, h and e are exact in the 2019 SI (CODATA 2022).
Light and every other electromagnetic wave travel at c = 299,792,458 m/s in a vacuum, so wavelength and frequency fix each other through c = fλ. Each photon carries energy E = hf = hc/λ, where h is Planck's constant. Enter any one of the three and the calculator returns the other two, plus the wavenumber, the energy per mole of photons and the band of the spectrum.
Students use it for photon-energy problems, and radio and optics work uses it to move between frequency and wavelength. Green light at 550 nm has a frequency of 5.45 × 10¹⁴ Hz and 2.25 eV per photon; the 2.45 GHz wave in a microwave oven is 12.2 cm long.
Wavelengths are vacuum values: inside glass or water, divide by the refractive index, while the frequency stays the same. Band edges are conventions that differ slightly between sources.
Checked against: Python 3.8 decimal with exact SI c, h, e: f = c/λ, E = hc/λ/e = 2.2542582 eV
Checked against: Python 3.8 decimal: λ = 299792458/2.45e9 = 0.1223643 m
Checked against: Python 3.8 decimal: λ = hc/(13.6 e) = 91.16485 nm (the Lyman limit is 91.2 nm)
Checked against: c/f = 2.99792458 m exactly (c is defined)
Divide the speed of light by the wavelength: f = c/λ, with c = 299,792,458 m/s and λ in metres. For 550 nm green light, f = 299,792,458 ÷ 0.000000550 = 5.45 × 10¹⁴ Hz, or 545 THz. The reverse is λ = c/f: an FM station at 100 MHz has a wavelength of 3.00 m.
Multiply Planck's constant by the frequency, E = hf, or divide hc by the wavelength, E = hc/λ, with h = 6.62607015 × 10⁻³⁴ J·s. In electronvolts, E = 1239.84 ÷ λ in nanometres, so a 700 nm red photon carries 1.77 eV and a 400 nm violet one 3.10 eV. h and the electron charge have been exact in the SI since 2019, and c since 1983.
About 380 to 750 nanometres, from violet to red; this calculator uses those edges for the visible band. Sources put the red end anywhere from 700 to 780 nm because eye sensitivity fades gradually; ISO 21348 uses 380–760 nm. Photon energies across the range run from 3.26 eV at 380 nm down to 1.65 eV at 750 nm.
About 12 cm. Microwave ovens run at 2.45 GHz, a wavelength of 12.24 cm, and 2.4 GHz Wi-Fi is 12.49 cm; 5 GHz Wi-Fi is 6.00 cm. Each 2.45 GHz photon carries 0.0000101 eV, over 200,000 times less than a green-light photon and far below the 13.6 eV needed to ionise a hydrogen atom, so microwaves heat food without ionising it.
The number of waves per centimetre, 1/λ, quoted in cm⁻¹ in infrared and Raman spectroscopy. From nanometres, the wavenumber is 10,000,000 ÷ λ: 550 nm is 18,182 cm⁻¹. An infrared band at 3,000 cm⁻¹, where C–H bonds stretch, lies at 3.33 µm. Wavenumber is proportional to photon energy, which is why spectroscopists use it as an energy scale.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “Green light, 550 nm” is checked against Python 3.8 decimal with exact SI c, h, e: f = c/λ, E = hc/λ/e = 2.2542582 eV.
CODATA 2022 — c, h and e are exact in the SI; NASA Science — Tour of the electromagnetic spectrum (band names and ranges); ISO 21348:2007 — Definitions of solar irradiance spectral categories.
6 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
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