Convert electrical potential energy to electron volts and joules. Essential for particle physics, nuclear science, spectroscopy, and accelerator design calculations.
Last Updated: 5/6/2026
Positive voltage = charge accelerated (gains energy); negative voltage = charge decelerated (loses energy). Typical ranges: ±1V (lab), ±50,000V (X-ray tube), ±1,000,000V (accelerator)
Electron or proton = 1 e; deuteron = 1 e; alpha particle (He²⁺) = 2 e; fully ionized C atom = 6 e
The electron volt (eV) is a fundamental unit of energy in atomic, nuclear, and particle physics, defined as the energy acquired by a single elementary charge (the charge of one electron or proton, magnitude 1.602176634 × 10⁻¹⁹ coulombs) when accelerated through a potential difference of exactly one volt in vacuum. Unlike the joule (which is vastly larger), the electron volt naturally matches the energy scales of atomic and subatomic phenomena: ionization of hydrogen requires 13.6 eV, X-ray photons range from 0.1 to 100 keV, gamma rays in nuclear decay span MeV to GeV, and cosmic ray particles reach PeV (10¹⁵ eV). The eV is perfect for particle physics because when scientists write that a collision produced a 5 GeV electron, they immediately know the particle is highly relativistic (rest mass of electron ≈ 0.511 MeV). The conversion between electrical potential and energy is direct and explicit in particle accelerator design: if you accelerate an electron through 1 million volts (1 MV), it gains exactly 1 million eV (1 MeV) of kinetic energy, a fundamental principle underlying PET scanners (511 keV photons from positron annihilation), medical X-ray production, and high-energy physics experiments at CERN's Large Hadron Collider.
The eV's widespread adoption stems from its mathematical elegance in relativistic calculations. In particle physics, energy, momentum, and mass all use eV as the base unit: the famous mass-energy equivalence E = mc² becomes simply E = mc² where mass is expressed in eV/c² (e.g., electron mass = 0.511 MeV/c²). Spectroscopy across disciplines relies on eV: UV-visible spectroscopy uses 1–5 eV photons, infrared spectroscopy 0.01–1 eV, microwave spectroscopy 10⁻⁶ eV, and gamma-ray astronomy deals with MeV–TeV photons. Modern particle detectors measure ionization energy (eV per electron-ion pair), scattering cross-sections (in barn units but energies in eV), and reaction Q-values (mass differences in eV/c²). Even in condensed matter physics, bandgaps, work functions, and binding energies are expressed in eV, universalizing communication across subfields. Understanding eV energy scales is indispensable for interpreting experimental data, designing accelerators, and developing detection systems.
Enter the potential difference in volts. Positive values accelerate the charge (energy gain); negative values decelerate it (energy loss). For an electron in a 50 kV X-ray tube, enter 50000 V (50 keV gain). For a deceleration scenario (e.g., electron beam on a target near ground), use negative voltage. Typical ranges: ±1V (lab), ±50,000V (spectroscopy), ±1,000,000V (accelerator).
Enter the charge as a multiple of the elementary charge (e = 1.602176634 × 10⁻¹⁹ C). Typical values: 1 for electron/proton/deuteron; 2 for alpha particle (He²⁺ nucleus); 6 for fully ionized carbon (C⁶⁺); 8 for oxygen ion (O⁸⁺). For multiply-charged ions used in heavy-ion beam detection, consult your accelerator control system for the ion's charge state.
The calculator displays E (eV) = q × V, the energy in electron volts. By definition, a particle with charge 1 e accelerated through 1 V gains exactly 1 eV of kinetic energy. This is the most commonly used unit in particle and nuclear physics. For a 5 keV photon, the result is 5000 eV or 5.000e+03 in scientific notation.
The calculator also shows energy in SI joules: E (J) = E (eV) × 1.602176634 × 10⁻¹⁹. Use joules when integrating with other SI quantities (e.g., calculating kinetic temperature from thermal energy, computing wavelength from photon energy λ = hc/E). For most particle physics work, stay in eV—it's cleaner and more intuitive.
Scenario: A diagnostic dental X-ray machine operates at 60 kV (60,000 volts). Electrons are accelerated through this potential and strike a tungsten target, producing bremsstrahlung (braking) radiation. A 50 keV X-ray photon is produced. Verify the energy in joules and calculate its wavelength for reference.
The eV naturally matches energy scales in atomic and particle phenomena (ionization ~eV, nuclear reactions ~MeV, cosmic rays ~GeV–PeV). Using joules requires writing numbers like 1.602 × 10⁻¹⁹, which is cumbersome. Moreover, in relativity, energy, momentum, and mass all use eV as a unified unit (mass in eV/c²), simplifying Lorentz-invariant calculations and cross-section computations.
For non-relativistic particles, E = qV is exact: it's the definition of the electron volt and directly from the work-energy theorem. For highly relativistic particles (e.g., electron at 10 MeV), the formula gives kinetic energy correctly, but total energy requires E_tot = √((pc)² + (mc²)²). Most applications (medical, spectroscopy) are non-relativistic; relativistic corrections matter only above ~MeV for electrons.
As of the 2019 SI Redefinition, the elementary charge is defined exactly as 1.602176634 × 10⁻¹⁹ C (fixed value, not measured). This makes the coulomb traceable to the ampere and second, with no experimental uncertainty. The eV conversion factor is therefore also exact by definition.
The formula E = qV works for any charge magnitude and sign. Quarks have charges of ±1/3 e or ±2/3 e, so a strange quark (−1/3 e) through 1 V field gains −1/3 eV. However, quarks are permanently confined inside hadrons and never exist freely in vacuum; this calculator applies to free particles and ions in accelerators.
Electron and proton: q = 1 e; Deuteron (proton + neutron nucleus): q = 1 e; Alpha particle (He-4 nucleus): q = 2 e; Carbon fully ionized (C⁶⁺): q = 6 e; Positron: q = 1 e (opposite sign in fields, but magnitude same). For ions, count the number of electrons removed or added to neutral atom.
For photons, E = hc/λ, so λ = hc/E. With Planck's constant h = 4.135667696 × 10⁻¹⁵ eV·s and c = 2.998 × 10⁸ m/s, hc ≈ 1240 eV·nm exactly (to 3 significant figures). This allows quick mental math: a 1 eV photon has λ ≈ 1240 nm (infrared), a 2 eV photon ≈ 620 nm (red visible light), a 4 eV photon ≈ 310 nm (UV). Invaluable for spectroscopy.
Thermal energy at room temp (~25°C): ~0.026 eV (26 meV). Visible photons: 1.5–3 eV. UV photons: 3–400 eV. X-rays: 100 eV–100 keV. Gamma rays: MeV–GeV. Cosmic rays: GeV–PeV (10¹⁵ eV). Nuclear magnetic resonance (NMR): 10⁻⁷ eV (GHz microwaves). This spectrum spans 22 orders of magnitude—eV notation keeps it manageable.
Mathematically, yes: E = qV with negative V gives negative energy. Physically, negative voltage means the particle loses energy (e.g., an electron retarded through −1000 V drops 1000 eV in kinetic energy). This is correct: the formula is energy change relative to a reference. In accelerators, voltage direction (positive for acceleration, negative for deceleration) determines sign.
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