Wavelength–Frequency–Energy Converter
Convert a photon’s wavelength, frequency, or energy and see all three side by side with steps and a mini spectrum.
Background
For a photon, the key relations are: c = λ·ν and E = h·ν = h·c / λ, where c ≈ 3.00×10⁸ m·s⁻¹ is the speed of light and h ≈ 6.63×10⁻³⁴ J·s is Planck’s constant. Knowing any one of λ, ν, or E lets you compute the other two.
How this calculator works
- Pick what you know: wavelength, frequency, or photon energy. The tool converts everything to SI units internally.
- Use core relations: we use c = λ·ν and E = h·ν = h·c / λ to find the missing quantities.
- Energy units: energy can be shown in J, eV, and kJ/mol (using Avogadro’s number).
- Regions of the spectrum: we classify the photon as radio, microwave, infrared, visible, ultraviolet, X ray, or gamma ray based on its wavelength.
Formula & Equations Used
Speed of light: c ≈ 3.00×10⁸ m·s⁻¹
Planck’s constant: h ≈ 6.63×10⁻³⁴ J·s
Wavelength–frequency relation: c = λ·ν, so ν = c / λ and λ = c / ν.
Photon energy: E = h·ν = h·c / λ.
Energy unit conversions: 1 eV = 1.602×10⁻¹⁹ J and E (kJ/mol) = E(J) × NA / 1000.
Example Problems & Step-by-Step Solutions
Example 1 — 500 nm green photon
Convert 500 nm to meters:
λ = 500×10⁻⁹ m = 5.00×10⁻⁷ m.
Frequency:
ν = c / λ ≈ 3.00×10⁸ / 5.00×10⁻⁷ ≈ 6.00×10¹⁴ Hz.
Energy:
E = h·ν ≈ 6.63×10⁻³⁴ × 6.00×10¹⁴ ≈ 4.0×10⁻¹⁹ J
which is about 2.5 eV.
Example 2 — 1.0 THz microwave
Frequency:
ν = 1.0 THz = 1.0×10¹² Hz.
Wavelength:
λ = c / ν ≈ 3.00×10⁸ / 1.0×10¹² = 3.0×10⁻⁴ m
which is 0.30 mm.
Energy:
E = h·ν ≈ 6.63×10⁻³⁴ × 1.0×10¹² = 6.63×10⁻²² J,
a very low energy photon.
Example 3 — 10 eV photon
Convert to joules:
E = 10 eV × 1.602×10⁻¹⁹ J/eV ≈ 1.60×10⁻¹⁸ J.
Frequency:
ν = E / h ≈ 1.60×10⁻¹⁸ / 6.63×10⁻³⁴ ≈ 2.4×10¹⁵ Hz.
Wavelength:
λ = c / ν ≈ 3.00×10⁸ / 2.4×10¹⁵ ≈ 1.25×10⁻⁷ m
which is 125 nm in the ultraviolet.
Frequently Asked Questions
Q: Can I use this for any kind of light?
Yes. The formulas apply to any photon, from radio waves to gamma rays. The only difference is the wavelength or frequency range.
Q: What units should I enter?
You can start from wavelength (nm, µm, m, Å), frequency (Hz to THz), or energy (eV, J, or kJ/mol). The calculator converts everything for you.
Q: Why do you classify the spectrum region?
The region label (radio, infrared, visible, ultraviolet, and so on) helps link the numbers to physical intuition and real world examples.
