Calculator
Example data table
| Energy (eV) | Wavelength (nm) | Frequency (Hz) | Spectroscopic (cm⁻¹) |
|---|---|---|---|
| 1 | 1239.841984 | 2.417989e+14 | 8065.54 |
| 2 | 619.920992 | 4.835978e+14 | 16131.09 |
| 10 | 123.984198 | 2.417989e+15 | 80655.44 |
| 100 | 12.398420 | 2.417989e+16 | 806554.39 |
Values assume vacuum propagation and exact SI constants.
Formula used
This calculator treats the input as photon energy in electronvolts and converts it to joules:
- E(J) = E(eV) × e, where e is the elementary charge.
- λ = h c / E (vacuum wavelength).
- ν = E / h, and ω = 2πν.
- Wavenumber: 1/λ (and spectroscopic cm⁻¹).
- Photon momentum: p = E / c.
Quick rule: λ(nm) ≈ 1239.841984 / E(eV).
How to use this calculator
- Enter the photon energy value.
- Select the energy unit (eV, keV, MeV, or GeV).
- Choose your preferred wavelength unit.
- Set decimals or enable scientific notation if needed.
- Click Calculate to view results above the form.
- Use the download buttons to export CSV or PDF.
Understanding electronvolts and photons
An electronvolt (eV) is the energy gained by one electron across one volt. Photon energy is often quoted in eV because it maps neatly to optical, ultraviolet, and X‑ray scales used in labs and datasheets.
Core conversion used by this tool
The calculator converts energy to joules using the elementary charge, then applies λ = h·c/E. With exact SI constants, the conversion stays consistent across eV, keV, MeV, and GeV inputs.
Handy constant for quick checks
For vacuum wavelengths, a useful shortcut is λ(nm) ≈ 1239.841984 / E(eV). This constant comes from h·c expressed in eV·nm, letting you sanity‑check results without a calculator.
Typical ranges across the spectrum
Visible light spans roughly 1.65–3.10 eV, which corresponds to about 750–400 nm. Near‑UV starts around 3.10 eV (≈400 nm). Soft X‑ray energies like 100 eV map to ≈12.4 nm, while 1 keV gives ≈1.24 nm.
Infrared examples: 0.50 eV corresponds to about 2480 nm (2.48 µm), and 0.10 eV is about 12.4 µm. Far‑IR and terahertz photons fall below 0.01 eV, giving wavelengths beyond 124 µm. At the other extreme, 10 keV produces roughly 0.124 nm.
Choosing output units wisely
Nanometers are convenient for visible and UV, micrometers for infrared, and ångström or nanometers for X‑rays. If you work in spectroscopy, compare wavenumber in cm⁻¹, which directly relates to many published line tables.
Derived quantities you also get
Beyond wavelength, the results include frequency ν = E/h, angular frequency ω = 2πν, period T = 1/ν, wavenumber 1/λ, and photon momentum p = E/c. These help connect energy to timing, phase, and propagation.
Practical tips for reliable results
Use scientific notation for extreme values, especially MeV or GeV energies where wavelengths fall into picometers or smaller. For materials, wavelength in a medium shortens by refractive index n, so λ_medium = λ_vacuum / n.
Remember this output is the vacuum wavelength, not the wavelength inside glass, water, or fiber. If you have a target wavelength and need the energy instead, invert the shortcut: E(eV) ≈ 1239.841984/λ(nm). Keep enough decimals when exporting for plotting. These ranges help pick practical wavelength units quickly.
FAQs
What wavelength corresponds to 2 eV?
In vacuum, 2 eV converts to about 620 nm because λ(nm) ≈ 1239.841984/2. Use the unit selector if you prefer µm or Å, and export the row for reports.
Is this conversion valid for electrons or ions?
No. The calculator uses photon relations (E = hν and λ = hc/E). For particles you would use the de Broglie wavelength, which depends on momentum, relativistic effects, and the particle’s mass.
Why does it assume vacuum propagation?
The formula uses the speed of light in vacuum. In a material with refractive index n, the wavelength shortens: λ_medium = λ_vacuum/n. Frequency stays the same if the photon energy is unchanged.
Which wavelength unit is best for X‑rays?
Ångström or nanometers are common. For example, 8 keV gives roughly 0.155 nm (about 1.55 Å). If you go above keV into MeV, wavelengths reach picometers or smaller, so enable scientific notation.
What is spectroscopic wavenumber in cm⁻¹?
It is 1/λ expressed per centimeter, widely used in IR and Raman tables. You can estimate energy from it with E(eV) ≈ 1.23984×10⁻⁴ × (cm⁻¹). Higher wavenumber means higher photon energy.
Why are my wavelengths extremely small at MeV?
Because energy and wavelength are inversely related. A 1 MeV photon corresponds to about 1.24 picometers in vacuum. Switch to meters or enable scientific notation to avoid losing precision from rounding.