Wavelength Calculator
Calculate wavelength (λ) from frequency and speed, find photon wavelength from energy (J / eV / kJ·mol⁻¹), or use Inverse mode to get frequency + energy from λ. Includes steps, quick picks, and a mini EM spectrum visual.
Background
Wavelength is the “length” of one wave cycle. For any wave, v = fλ. For light in vacuum, c = fλ. For photons, energy relates to wavelength via E = hc/λ.
How to use this calculator
- Pick a mode: Wave (v & f), EM (f & c), Photon (E & hc), or Inverse (λ → f & E).
- Enter values and choose units.
- Click Calculate to get clean results + unit conversions.
- Use Quick picks to sanity-check common cases.
How this calculator works
- It first converts your inputs into standard units (Hz, m/s, meters, joules) so calculations stay consistent.
- Then it applies the correct relationship for your mode: Wave uses speed + frequency, EM uses the speed of light (and optional n), and Photon ties energy to wavelength.
- In Inverse mode, you enter λ, and we compute frequency and photon energy (plus eV and kJ/mol conversions).
- Finally, the calculator shows friendly unit conversions (nm/µm/m), adds a visible-color label when λ is 380–700 nm, and labels the EM spectrum region (IR/visible/UV/etc.) when relevant.
Formula & Equation Used
Wave relation:
Wavelength from frequency:
Photon energy relation:
Wavelength from energy:
Example Problems & Step-by-Step Solutions
Example 1 — Sound wave
A sound wave in air travels at 343 m/s with frequency 440 Hz.
λ = v/f = 343/440 = 0.7795 m.
Example 2 — Visible light from frequency
Light has frequency 5.00×1014 Hz.
λ = c/f = (3.00×108)/(5.00×1014) = 6.00×10−7 m = 600 nm.
Example 3 — Photon wavelength from energy
A photon has energy 2.48 eV.
λ ≈ 1240 eV·nm / 2.48 eV = 500 nm.
Example 4 — Inverse (λ → f and E)
A green laser has wavelength 532 nm.
f = c/λ = (3.00×108)/(5.32×10−7) ≈ 5.64×1014 Hz.
E = hf ≈ 3.74×10−19 J ≈ 2.33 eV.
Frequently Asked Questions
Q: Why do I get different λ in a medium?
Because light slows down in a medium: v = c/n, so λ decreases while frequency stays the same.
Q: What’s the fastest way to convert eV ↔ nm?
Use E(eV) ≈ 1240 / λ(nm) (equivalently λ(nm) ≈ 1240 / E(eV)).
Q: Does frequency change when light enters water?
No — frequency stays the same at the boundary; speed and wavelength change.