Convert between electron-volts, joules, temperature, and photon wavelength. Includes voltage-to-energy conversion, particle rest mass table, relativistic speed calculation, and 10 energy units.
The electron-volt (eV) is the energy gained by a single electron accelerated through a potential difference of one volt: 1 eV = 1.602 × 10⁻¹⁹ joules. Despite its name, the electron-volt is a unit of energy — not voltage — and is the preferred unit in atomic, nuclear, and particle physics because energies at these scales are conveniently expressed in eV rather than tiny fractions of a joule.
The electron-volt connects voltage, energy, temperature, and photon wavelength through fundamental constants. An energy of 1 eV corresponds to a temperature of about 11,600 K, a photon wavelength of 1240 nm (near infrared), and the kinetic energy of an electron at rest accelerated through 1 volt. These conversions are used daily in spectroscopy, semiconductor physics, medical imaging, and high-energy physics.
This calculator converts between 10 energy units (eV, keV, MeV, GeV, TeV, meV, J, kJ, cal, erg), computes equivalent temperature and photon properties, calculates voltage-to-energy for charged particles, and shows relativistic speeds for five common particles at any given energy.
Converting between electron-volts and other energy units requires memorizing several fundamental constants (e, h, k_B, c). Adding mass-energy equivalence and relativistic kinematics makes manual calculations tedious and error-prone. This calculator handles all conversions and provides a particle reference table with relativistic speeds. Keep these notes focused on your operational context.
Energy (eV) from Voltage: E = q × V (eV for charge q in units of e) Conversions: 1 eV = 1.602 × 10⁻¹⁹ J E (J) = E (eV) × 1.602 × 10⁻¹⁹ Temperature: T = E / k_B (k_B = 1.381 × 10⁻²³ J/K) Photon Frequency: f = E / h (h = 6.626 × 10⁻³⁴ J·s) Photon Wavelength: λ = hc / E (hc = 1240 eV·nm) Relativistic: γ = 1 + KE / mc² β = √(1 − 1/γ²)
Result: 2 eV = 3.204 × 10⁻¹⁹ J, T = 23,200 K, λ = 620 nm (red light)
An energy of 2 eV equals 2 × 1.602×10⁻¹⁹ = 3.204×10⁻¹⁹ J. The equivalent temperature is 2 × 11,604 = 23,209 K. A photon of this energy has wavelength λ = 1240/2 = 620 nm, which is visible red light. An electron with 2 eV kinetic energy moves at about 0.28% the speed of light.
Atomic and molecular spectroscopy directly measures energy level differences in electron-volts. The hydrogen atom's ground-state ionization energy is 13.6 eV. Visible photon energies range from 1.65 eV (red, 750 nm) to 3.1 eV (violet, 400 nm). X-ray emission lines from inner-shell electron transitions have energies of keV, and nuclear gamma rays reach MeV. The electron-volt provides a natural scale for all these phenomena.
In semiconductor physics, the band gap energy (in eV) determines a material's electronic and optical properties. Silicon's indirect band gap is 1.12 eV (infrared), gallium arsenide's direct gap is 1.42 eV (near IR), and gallium nitride's gap is 3.4 eV (UV). LEDs and laser diodes emit photons with energy approximately equal to the band gap, making eV the natural unit for optoelectronic device design.
Particle accelerators are characterized by the energy they impart to particles, measured in eV. Medical linacs operate at 6-20 MeV, synchrotron light sources at hundreds of MeV to several GeV, and the Large Hadron Collider (LHC) at 6.8 TeV per beam. At these energies, particles travel at 99.9999991% the speed of light, and the distinction between kinetic energy and rest mass energy becomes essential.
Energy. Despite the name, 1 eV is the amount of kinetic energy gained by a single electron (charge e = 1.602×10⁻¹⁹ C) when accelerated through a potential difference of 1 volt. In SI: 1 eV = 1.602×10⁻¹⁹ joules.
Because particle-scale energies are inconveniently small in joules. A photon of visible light has about 2 eV (= 3.2×10⁻¹⁹ J). Working in eV eliminates the need for 10⁻¹⁹ factors and makes orders of magnitude intuitive: keV for X-rays, MeV for nuclear, GeV for particle physics.
Divide by Boltzmann's constant: T = E / k_B. In convenient units: 1 eV ≈ 11,604 K. This is useful in plasma physics and semiconductor physics where thermal energy kT determines carrier behavior.
Einstein's E = mc² means mass can be expressed in energy units. The electron has a rest mass energy of 0.511 MeV (= 8.2×10⁻¹⁴ J). Particle physicists express mass in MeV/c² or GeV/c² as standard practice.
It assumes the input energy is the particle's kinetic energy (not total energy). The Lorentz factor is γ = 1 + KE/(mc²), and the speed is β = v/c = √(1 − 1/γ²). For electrons at keV energies, this gives significantly relativistic speeds; protons need MeV energies to become relativistic.
The product hc = 6.626×10⁻³⁴ × 2.998×10⁸ = 1.240×10⁻⁶ eV·m = 1240 eV·nm. This means λ(nm) = 1240 / E(eV) — an instant photon wavelength lookup. For example, 2 eV → 620 nm (red), 3 eV → 413 nm (violet).