Wavelength, Frequency & Photon Energy Calculator
Enter any one of wavelength, frequency, photon energy or wavenumber and get the other three, plus the energy in electronvolts, joules and kilojoules per mole. The calculator names the band of the electromagnetic spectrum — and the colour, for visible light — and marks it on a spectrum bar. It uses the exact SI values of c, h and e. Free, no sign-up.
Results
532 nm
Wavelength
563.5 THz
Frequency
2.331 eV
Photon energy
3.734 × 10⁻¹⁹ J
Photon energy in joules
224.9 kJ/mol
Energy per mole of photons
18800 cm⁻¹
Wavenumber
Band
Visible — green
The working
- f = c ÷ λ = 299 792 458 m/s ÷ 532 nm = 563.5 THz
- E = h × f = 6.62607015 × 10⁻³⁴ J·s × 563.5 THz = 3.734 × 10⁻¹⁹ J
- E = 3.734 × 10⁻¹⁹ J ÷ 1.602176634 × 10⁻¹⁹ J/eV = 2.331 eV
Uses the exact SI values c = 299 792 458 m/s, h = 6.626 070 15 × 10⁻³⁴ J·s, e = 1.602 176 634 × 10⁻¹⁹ C and N = 6.022 140 76 × 10²³ per mole. Wavelengths are in vacuum.
How to Use the Wavelength, Frequency and Photon Energy Calculator
- 1. Say what you know. Choose wavelength, frequency, photon energy or wavenumber. Wavenumber, in cm⁻¹, is the unit used in infrared and Raman spectroscopy.
- 2. Type the value and pick its unit. Wavelengths run from picometres, ångströms and nanometres to kilometres; frequencies from Hz to EHz; energies in µeV to GeV, joules or kJ/mol.
- 3. Read the conversions. The other three quantities appear together with the energy in eV, joules and kJ/mol, plus the band name and, for visible light, an approximate colour swatch.
- 4. Check the working. Each formula is written with your numbers, and the spectrum bar marks where the value sits between gamma rays and radio waves.
The Relationships
| Relationship | Formula | Notes |
|---|---|---|
| Frequency from wavelength | f = c ÷ λ | c = 299,792,458 m/s (exact) |
| Photon energy from frequency | E = h × f | h = 6.626 070 15 × 10⁻³⁴ J·s (exact) |
| Photon energy from wavelength | E = h × c ÷ λ | hc = 1239.842 eV·nm |
| Energy in electronvolts | E(eV) = E(J) ÷ 1.602 176 634 × 10⁻¹⁹ | e is exact |
| Wavenumber | ν̃ = 1 ÷ λ | Usually quoted in cm⁻¹ |
| Per mole of photons | E × N | N = 6.022 140 76 × 10²³ per mole (exact) |
Since the 2019 redefinition of the SI, c, h, e and the Avogadro constant all have exact defined values, so these conversions carry no uncertainty from the constants — only from your input. The most useful shortcut is hc = 1239.84 eV·nm: divide it by a wavelength in nanometres to get the photon energy in electronvolts, so 500 nm light carries 2.48 eV. Frequency, wavelength and energy are linked one to one, which is why the calculator can start from any of them.
The Electromagnetic Spectrum
| Band | Wavelength | Frequency | Photon energy |
|---|---|---|---|
| Radio | above about 1 m | below 300 MHz | below 1.24 µeV |
| Microwave | about 1 mm to 1 m | 300 MHz to 300 GHz | 1.24 µeV to 1.24 meV |
| Infrared | 750 nm to about 1 mm | 300 GHz to 400 THz | 1.24 meV to 1.65 eV |
| Visible | 380 to 750 nm | 400 to 790 THz | 1.65 to 3.26 eV |
| Ultraviolet | 10 to 380 nm | 790 THz to 30 PHz | 3.26 to 124 eV |
| X-rays | 10 pm to 10 nm | 30 PHz to 30 EHz | 124 eV to 124 keV |
| Gamma rays | below 10 pm | above 30 EHz | above 124 keV |
These boundaries are conventions, and they shift between fields: the eye's sensitivity fades gradually near 380 and 750 nm, and X-rays and gamma rays are often distinguished by origin rather than energy. Radio frequencies below 300 MHz are further split into the ITU bands from ELF to VHF, and the calculator names the ITU band (UHF, SHF, EHF and so on) for microwave frequencies as well. Infrared is divided into near (to 3 µm), mid (3–50 µm) and far infrared, and ultraviolet into UV-A, UV-B and UV-C.
Worked Examples
- A green laser pointer, 532 nm (the starting example): f = 299,792,458 ÷ 532 × 10⁻⁹ = 563.5 THz, E = 3.734 × 10⁻¹⁹ J = 2.331 eV, which is 224.9 kJ/mol, and the wavenumber is about 18,800 cm⁻¹. It is visible green light.
- FM radio at 100 MHz: λ = 299,792,458 ÷ 100 × 10⁶ = 2.998 m, with a photon energy of only 0.4136 µeV. It is a radio wave in the VHF band.
- The hydrogen 21 cm line, 1420.405751768 MHz: λ = 21.106 cm and E = 5.874 µeV, in the UHF band, which radio astronomers use to map hydrogen in the galaxy.
- A 60 keV diagnostic X-ray: λ = 1239.84 ÷ 60,000 nm = 20.66 pm, a frequency of 14.5 EHz.
Wavelength in a medium
All wavelengths here are in vacuum. When light enters glass or water its frequency and photon energy stay the same, but its speed drops by the refractive index n, so its wavelength becomes λ ÷ n. Tables of laser lines are given in vacuum or in air, which differ by about 0.03%.
Frequently Asked Questions
- How do I convert wavelength to frequency?
- Divide the speed of light by the wavelength: f = c ÷ λ, with c = 299,792,458 m/s and λ in metres. A 600 nm wave has f = 299,792,458 ÷ 6 × 10⁻⁷ ≈ 5.0 × 10¹⁴ Hz, or 500 THz.
- How do I convert wavelength in nm to energy in eV?
- Divide 1239.84 by the wavelength in nanometres: E(eV) = 1239.84 ÷ λ(nm). For 400 nm violet light that gives 3.10 eV, and for 700 nm red light it gives 1.77 eV.
- What is the formula for the energy of a photon?
- E = h × f = h × c ÷ λ, where h is the Planck constant, 6.626 070 15 × 10⁻³⁴ J·s. Shorter wavelengths and higher frequencies mean more energy per photon, which is why ultraviolet can damage skin and radio waves cannot.
- What is the range of visible light?
- Roughly 380 to 750 nm, or about 400 to 790 THz, from violet to red. The limits are not sharp — the eye's response fades at both ends — so you will also see 400–700 nm and 380–780 nm in textbooks.
- What is a wavenumber and why do spectroscopists use it?
- The wavenumber is the number of waves per unit length, ν̃ = 1 ÷ λ, usually in reciprocal centimetres. It is proportional to energy, so molecular vibration spectra read off directly in cm⁻¹; 1000 cm⁻¹ corresponds to a 10 µm wavelength.
- Why does the calculator show kJ/mol?
- Chemists compare photon energy to bond energies, which are quoted per mole. Multiplying a photon's energy by the Avogadro constant gives the energy of a mole of photons: 532 nm light carries about 225 kJ/mol, enough to break weak bonds.