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.
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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.
Every electromagnetic wave obeys c = fλ: frequency times wavelength equals the speed of light, exactly 299,792,458 m/s in a vacuum. So f = c/λ and λ = c/f. An FM station at 100 MHz has λ = 299,792,458 ÷ 100,000,000 ≈ 2.998 m. The shorter the wavelength, the higher the frequency.
The speed of light in vacuum is exactly c = 299,792,458 m/s. Since 1983 the meter has been defined from this number, so it carries no measurement uncertainty (BIPM definition of the meter). In other units:
The familiar 300,000 km/s is a rounding, 0.07% too high. At the exact value, light crosses one astronomical unit (149,597,870,700 m, close to the average Earth–Sun distance) in 499 seconds, about 8 minutes 19 seconds.
Light is slower inside glass, water or air: its speed there is c/n, where n is the material's refractive index.
Convert the wavelength to meters, then divide c by it. Green light at 550 nm is 550 × 10⁻⁹ m, so f = 299,792,458 ÷ 0.000000550 ≈ 5.45 × 10¹⁴ Hz, or 545 THz.
The prefixes to watch: 1 nm = 10⁻⁹ m and 1 µm = 10⁻⁶ m; 1 MHz = 10⁶ Hz, 1 GHz = 10⁹ Hz and 1 THz = 10¹² Hz.
| Known quantity | Wavelength (m) | Frequency (THz) | Photon energy (eV) |
|---|---|---|---|
| 550 nm | 5.5e-7 | 545.077 | 2.25426 |
| 100 MHz | 2.99792 | 0.0001 | 4.13567e-7 |
| 2.45 GHz | 0.122364 | 0.00245 | 0.0000101324 |
| 1000 eV | 1.23984e-9 | 241799 | 1000 |
Values are rounded to six significant digits. Notation such as 5.5e-7 means 5.5 × 10⁻⁷.
Divide c by the frequency in hertz. A microwave oven's 2.45 GHz gives λ = 299,792,458 ÷ 2,450,000,000 ≈ 0.1224 m, about 12.24 cm. Doubling the frequency halves the wavelength, because c stays fixed.
Spectrum bands are named by vacuum wavelength. The edges below are conventions, and sources draw them slightly differently.
Each photon carries E = hf, or E = hc/λ, where Planck's constant is exactly h = 6.62607015 × 10⁻³⁴ J·s. Divide joules by 1.602176634 × 10⁻¹⁹ to get electronvolts: a 550 nm photon carries about 2.254 eV.
A handy shortcut is E (eV) ≈ 1239.84 ÷ λ (nm). Rearranged, λ (nm) ≈ 1239.84 ÷ E (eV), so a 1,000 eV X-ray photon has λ ≈ 1.24 nm.
That is the energy of one photon. A beam's power also depends on how many photons arrive each second, so wavelength alone says nothing about brightness.
Wavenumber is 1/λ, quoted in cm⁻¹ in spectroscopy. From nanometers it is 10,000,000 ÷ λ, so 550 nm is 18,182 cm⁻¹. The angular wavenumber of wave equations, 2π/λ, is a different quantity.
Energy per mole of photons multiplies one photon's energy by the Avogadro constant, 6.02214076 × 10²³ mol⁻¹. A mole of 550 nm photons carries about 217.5 kJ, and 1 eV per photon corresponds to 96.485 kJ/mol.
For refraction and lenses, use the thin lens and Snell's law calculator. To change frequency or energy units alone, use the frequency converter or the energy converter.
Checked against: With exact SI c, h, e: f = c/λ, E = hc/λ/e = 2.2542582 eV
Checked against: λ = 299792458/2.45e9 = 0.1223643 m
Checked against: 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.
This calculator includes 6 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.