Enter particle motion data
Use the relativistic model for speeds approaching light speed.
For a massive particle, the entered speed must be below 1 c.
Example Data Table
| Particle | Mass | Speed | Model | Approximate kinetic energy |
|---|---|---|---|---|
| Electron | 1 mₑ | 1.00 × 10⁶ m/s | Classical | 2.84 eV |
| Proton | 1 mₚ | 1.00 × 10⁶ m/s | Classical | 5.22 keV |
| Electron | 1 mₑ | 0.80 c | Relativistic | 340.7 keV |
| Alpha particle | 4.00 u | 2.00 × 10⁶ m/s | Classical | 82.9 keV |
Formula Used
Classical kinetic energy: KE = ½mv²
Relativistic kinetic energy: KE = (γ − 1)mc²
Lorentz factor: γ = 1 / √(1 − v²/c²)
Electron volt conversion: Energy in eV = Energy in J ÷ 1.602176634 × 10⁻¹⁹
Here, m is mass in kilograms, v is speed in metres per second, and c is the speed of light. The classical equation is best at low speeds. The relativistic equation is required when speed becomes a notable fraction of c.
How to Use This Calculator
- Choose the classical or relativistic calculation model.
- Select a particle preset, or keep Custom mass for your own value.
- Enter mass and choose its unit carefully.
- Enter speed, then choose the matching speed unit.
- Select the number of significant figures for displayed results.
- Press Calculate Energy to place the result above this form.
- Use the CSV or PDF button after a successful calculation.
Understanding Kinetic Energy in Electron Volts
Kinetic energy describes the energy carried by motion. In laboratory work, joules are often too large or too awkward for particles. Electron volts provide a convenient scale. One electron volt is the energy gained by one elementary charge moving through one volt. This calculator converts a motion result into electron volts. It also returns joules, kiloelectron volts, megaelectron volts, and relativistic values.
A classical calculation works well when speed is much lower than light speed. It uses one half of mass multiplied by velocity squared. The square is important. Doubling speed raises classical kinetic energy by four times. Doubling mass raises it by two times. Classical estimates work for slow ions, molecules, and everyday objects. They become unreliable as velocity approaches the speed of light.
Relativistic kinetic energy handles high speed motion. It uses the Lorentz factor, called gamma. Gamma increases slowly at first. It rises sharply near light speed. A particle with mass cannot reach or exceed light speed. The energy required grows without limit. This explains why calculations need a relativistic model. Select that model whenever the speed is a meaningful fraction of c.
Mass units also require care. Kilograms are the standard physics unit. Atomic mass units are helpful for atoms and ions. Electron and proton mass units simplify particle problems. The calculator converts every choice into kilograms before solving. Speed units follow the same approach. You may enter metres per second, kilometres per second, kilometres per hour, or a fraction of light speed. Check that each unit matches the number entered.
The result is shown in electron volts because particle energies span large ranges. Small electron energies may fit in eV. Atomic transitions often use eV or keV. Nuclear processes often use MeV. High energy experiments may use GeV. The calculator presents the direct eV value first. It then provides a scaled value for easier reading. Joules remain available for comparison with systems.
Use sensible significant figures. Input data rarely justify decimal places. Three or four significant figures suit most teaching problems. Higher precision is useful only when the mass and speed are known accurately. Avoid rounding the velocity before a relativistic calculation. Small changes near light speed can produce energy changes. Preserve the original measurement until the final result.
Compare the model outputs when learning. At low speed, classical and relativistic values agree. The difference grows with beta, where beta equals velocity divided by light speed. Gamma is always at least one. A gamma near one means relativistic effects are small. A larger gamma signals stronger effects. These checks help identify selection mistakes and unrealistic entries.
The calculator works for electrons, protons, neutrons, alpha particles, and custom masses. It does not include potential energy, binding energy, radiation loss, or collisions. Those effects may matter in real devices. Treat this result as translational kinetic energy for one particle. Record the units and model beside every calculation.
Frequently Asked Questions
What is an electron volt?
An electron volt, written eV, is a small unit of energy. It equals 1.602176634 × 10⁻¹⁹ joules. It is widely used for electrons, atoms, ions, photons, and particle beams.
When should I use the classical model?
Use the classical model when speed is far below light speed. It is usually suitable for ordinary mechanical systems and many slow particle problems. It becomes less accurate as speed rises toward c.
When is the relativistic model necessary?
Use the relativistic model when speed is a noticeable fraction of light speed. It is the safer choice for fast electrons and accelerator particles. The classical equation then underestimates kinetic energy.
Can I enter a fraction of light speed?
Yes. Choose Fraction of light speed (c), then enter a value below 1. For example, enter 0.75 for seventy-five percent of light speed.
Why must the entered speed stay below c?
A particle with rest mass cannot reach light speed. The relativistic energy equation becomes undefined at c. The required energy rises without limit as speed approaches c.
Does the calculator include rest energy?
No. The displayed value is kinetic energy only. Relativistic rest energy, mc², is not included in the reported kinetic energy. The formula uses the energy above rest energy.
What does gamma mean?
Gamma is the Lorentz factor. It measures how strongly relativistic effects change motion. Gamma equals one at rest and increases as speed approaches light speed.
Can I calculate energy for an atom or ion?
Yes. Enter the particle mass in atomic mass units or kilograms. The result describes translational kinetic energy. It does not automatically include internal, ionization, or binding energies.
Why are both eV and joules shown?
Electron volts are convenient for particles. Joules connect the result with SI calculations and macroscopic energy values. Showing both helps you verify conversions and compare scales.
How many significant figures should I select?
Use three or four figures for typical homework or measured data. Use more only when your inputs have matching accuracy. Extra digits cannot improve uncertain measurements.
Can this result describe collision energy?
It describes one particle's translational kinetic energy in the selected frame. Collision energy can require momentum conservation, centre-of-mass calculations, target motion, and additional energy losses.
Accurate energy estimates support safer, clearer particle physics decisions.