How this instrument works
The electron-volt is a unit of energy, not of voltage, and this sheet is really just the definition written out as arithmetic. When a charge q falls through a potential difference V, the electric field does work W = qV on it, and that work becomes kinetic energy. Express q as a multiple of the elementary charge e rather than in coulombs, and express the answer in electron-volts rather than joules, and the elementary charge cancels from both sides: E(eV) = V × q. No constant needs typing in, because the unit itself was built to absorb it.
That cancellation is why the formula looks almost too simple. It is not an approximation of something messier — the work-energy relationship for a charge crossing a field is exact at any speed, since it is bookkeeping about energy transferred, not a statement about how fast the particle ends up moving. A time-of-flight mass spectrometer relies on precisely this: the accelerating voltage in the source region fixes each ion's kinetic energy before it ever enters the drift tube, and that energy is what the flight-time measurement downstream is built on.
The one place people go wrong is the charge state itself. Charge, in multiples of e, means the particle's net ionization, not its atomic mass or atomic number. A proton or an electron carries 1; an alpha particle, a helium nucleus stripped of both electrons, carries 2; a fully stripped carbon ion carries 6. Mistake mass number for charge state and the energy reading comes out scaled by whatever number was substituted in error — a real failure mode in accelerator and ion-source work, where multiply-charged species are routine.
- Enter the potential difference the particle crosses into Accelerating voltage, choosing V or kV from the unit menu.
- Set Charge, in multiples of e to the particle's net charge state — 1 for an electron or proton, 2 for a doubly ionized ion, and so on.
- Read Kinetic energy, eV directly. No hidden constant is applied; the arithmetic is just voltage times charge state.
- For joules instead of electron-volts, multiply the Kinetic energy, eV reading by 1.602176634 × 10⁻¹⁹, the exact elementary charge.
Worked example — a single electron across 100 volts
Set Accelerating voltage to 100 V and Charge, in multiples of e to 1 — a lone electron, the simplest case there is. Kinetic energy, eV reads 100.0 eV directly, with no multiplication by any hidden constant, because a volt and an electron-volt are related by exactly one elementary charge crossing exactly one volt. That is not a measured coincidence; it is how the electron-volt is defined in the first place.
Raise Charge, in multiples of e to 2 — an alpha particle, a helium nucleus stripped of both electrons — while leaving Accelerating voltage at 100 V, and Kinetic energy, eV doubles to 200 eV. The same 100 V now buys twice the energy, because voltage measures energy per unit charge: a particle carrying two elementary charges collects two shares of that 100 eV, not one doubled share of something else.
Push Accelerating voltage to 1,000 V with Charge, in multiples of e back at 1, and Kinetic energy, eV reads 1,000 eV — one keV, the scale that names X-ray tubes and sets the photon energies produced when an electron accelerated through that potential strikes a target.
Questions
What exactly is an electron-volt?
A unit of energy, not of voltage: the kinetic energy one elementary charge gains crossing a one-volt potential difference. It equals exactly 1.602176634 × 10⁻¹⁹ joules since the 2019 SI redefinition fixed the elementary charge's value. Physicists and semiconductor engineers use it because it is the natural energy scale of a single accelerated charge, avoiding the tiny joule figures ordinary SI arithmetic would otherwise produce.
Why doesn't the formula need any physical constants typed in?
Because both sides are already expressed in matching units. Kinetic energy equals charge times voltage, E = qV, in joules when q is in coulombs and V in volts. Express q instead as a multiple of the elementary charge and E in electron-volts, and that constant cancels entirely, leaving E(eV) = V × q. The elementary charge has not vanished — it is simply built into the electron-volt's definition.
What does charge, in multiples of e, actually mean?
The particle's net charge state, not its mass or atomic number. An electron or proton carries 1, an alpha particle (a helium nucleus stripped of both electrons) carries 2, and a fully stripped carbon ion carries 6. Enter that small integer, not the ion's atomic mass — confusing the two is a common mistake and inflates the energy reading by whatever multiple the mass was substituted for.
Does this conversion still hold at relativistic speeds?
Yes, because it counts energy, not velocity. E = qV is the work an electric field does on a charge, and that bookkeeping holds at any speed; what changes near light speed is the relationship between that energy and the particle's actual speed, which needs a separate relativistic formula. A 500 keV electron's energy from this sheet is exact even though its speed is no longer simply proportional to voltage.
Where does this conversion actually get used?
In any instrument that accelerates charged particles through a set voltage and reports the resulting energy: time-of-flight mass spectrometers, where the accelerating voltage fixes ion kinetic energy before the drift tube; X-ray tubes, where tens of kilovolts set electron energy before impact; and particle accelerator stages, quoted in keV or MeV because those numbers stay human-sized.
How do I get the answer in joules instead of electron-volts?
Multiply the Kinetic energy, eV reading by the elementary charge, exactly 1.602176634 × 10⁻¹⁹ coulombs since the 2019 SI redefinition. A 100 eV result becomes 1.602176634 × 10⁻¹⁷ J. That constant carries no measurement uncertainty at all — it is fixed by definition, so the joule figure is exactly as trustworthy as the electron-volt one.