Electromagnetic Radiation — Wavelength, Frequency & Photon Energy
Light and all electromagnetic (EM) waves in vacuum satisfy
the fundamental relation
\[
c = \lambda\,\nu
\]
where \(c=299\,792\,458\ \mathrm{m\,s^{-1}}\) (exact) is the speed of light,
\( \lambda \) is wavelength, and \( \nu \) is frequency.
Knowing one determines the other: \( \lambda = \dfrac{c}{\nu} \) and \( \nu = \dfrac{c}{\lambda} \).
Photon energy
For a single photon of the radiation,
\[
E = h\,\nu = \frac{h\,c}{\lambda},
\qquad
h = 6.62607015\times10^{-34}\ \mathrm{J\,s}
\]
Sometimes energy is reported in electronvolts:
\(1\ \mathrm{eV} = 1.602176634\times10^{-19}\ \mathrm{J}\).
Units you will see in the calculator
- Wavelength \( \lambda \): m, cm, mm, μm, nm, and Å (ångström).
\(1\ \mathrm{cm}=10^{-2}\ \mathrm{m}\), \(1\ \mathrm{μm}=10^{-6}\ \mathrm{m}\),
\(1\ \mathrm{nm}=10^{-9}\ \mathrm{m}\), \(1\ \text{Å}=10^{-10}\ \mathrm{m}\).
- Frequency \( \nu \): Hz, kHz, MHz, GHz, THz, PHz
(powers of \(10^{3}\)).
- Energy \(E\): J and eV.
Spectral bands and visible colors
The tool also classifies the radiation by its wavelength in vacuum. Boundaries are conventional and approximate:
| Band / Color | Typical wavelength range | Typical frequency range |
|---|
| Gamma rays | < \(10^{-11}\ \mathrm{m}\) | > \(3\times10^{19}\ \mathrm{Hz}\) |
| X-rays | \(10^{-11}\)–\(10^{-8}\ \mathrm{m}\) | \(3\times10^{16}\)–\(3\times10^{19}\ \mathrm{Hz}\) |
| Ultraviolet (UV) | \(10^{-8}\)–\(3.8\times10^{-7}\ \mathrm{m}\) | \(8\times10^{14}\)–\(3\times10^{16}\ \mathrm{Hz}\) |
| Visible (approx.) | \(380\)–\(750\ \mathrm{nm}\) | \(4\times10^{14}\)–\(8\times10^{14}\ \mathrm{Hz}\) |
| Infrared (IR) | \(7.5\times10^{-7}\)–\(10^{-3}\ \mathrm{m}\) | \(3\times10^{11}\)–\(4\times10^{14}\ \mathrm{Hz}\) |
| Microwave | \(10^{-3}\)–\(1\ \mathrm{m}\) | \(3\times10^{8}\)–\(3\times10^{11}\ \mathrm{Hz}\) |
| Radio | \(>\ 1\ \mathrm{m}\) | \(<\ 3\times10^{8}\ \mathrm{Hz}\) |
Within the visible band, a common approximate mapping is:
380–450 nm (violet), 450–495 nm (blue), 495–570 nm (green),
570–590 nm (yellow), 590–620 nm (orange), 620–750 nm (red).
Perceived color also depends on intensity and context.
How the calculator works
- Select whether you know \( \lambda \) or \( \nu \), choose the input unit, and enter a value.
- The tool converts to SI, applies \( c=\lambda\nu \) to find the unknown, and converts both to
several convenient units.
- It computes the photon energy \(E\) in J and eV and classifies the radiation by band/color.
Note on media: The relation \(c=\lambda\nu\) holds with
\(c\) replaced by the phase speed in the medium \(v=\dfrac{c}{n}\), where \(n\) is the
refractive index. The calculator assumes vacuum; in materials,
wavelengths shorten by \(1/n\) while frequency stays the same.
