Energy to Wavelength Calculator
Convert photon energy to wavelength and frequency using Planck's constant and the speed of light.
What Is the Energy-Wavelength Relationship?
Photons carry discrete packets of energy tied directly to their wavelength. Shorter wavelengths mean higher energy, while longer wavelengths mean lower energy. This inverse relationship shows up in spectroscopy, lasers, X-rays, and anywhere you need to connect a photon's color or frequency to its energy.
Energy to Wavelength Formula
$$E = h \times f = \frac{h \times c}{\lambda}$$Rearranged to solve for wavelength:
$$\lambda = \frac{h \times c}{E}$$Here \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) J·s), \(c\) is the speed of light (\(2.998 \times 10^{8}\) m/s), \(E\) is photon energy in joules, and \(\lambda\) is wavelength in meters. A handy shortcut in nanometers and electronvolts is \(\lambda_{\text{nm}} \approx 1240 / E_{\text{eV}}\).
When to Use This Calculator
Use it when you know a photon's energy from a transition, band gap, or laser specification and need the corresponding wavelength or frequency. It also works in reverse: enter a wavelength to find photon energy. Related tools: Wavelength Calculator and Photon Energy Calculator.
Frequently Asked Questions
What happens to energy when wavelength decreases?
Photon energy increases. Energy is inversely proportional to wavelength, so halving the wavelength doubles the energy.
What units should I use for energy?
Joules are the SI unit. Electronvolts (eV) are common in atomic and solid-state physics. This calculator accepts J, eV, keV, and MeV and converts internally.
How do I convert wavelength in nanometers to energy?
Switch to wavelength-to-energy mode, enter the value in nanometers, and the tool computes energy in eV and joules using \(E = hc/\lambda\).
Does this apply only to light in a vacuum?
The formulas use the vacuum speed of light. In a medium, wavelength changes but photon energy (set at emission) stays the same.
What is the relationship between frequency and energy?
Photon energy equals Planck's constant times frequency: \(E = hf\). Frequency and wavelength relate through \(f = c/\lambda\).
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