Calculator Form
Example Data Table
| Particle | Rest Mass | Input Mode | Input | Total Energy | Kinetic Energy |
|---|---|---|---|---|---|
| Electron | 0.511 MeV/c² | Velocity | 0.80 c | 0.852 MeV | 0.341 MeV |
| Proton | 938.272 MeV/c² | Lorentz Factor | γ = 3.00 | 2814.816 MeV | 1876.544 MeV |
| Muon | 105.658 MeV/c² | Momentum | 500 MeV/c | 511.046 MeV | 405.388 MeV |
Formula Used
Lorentz factor: γ = 1 / √(1 - v²/c²)
Rest energy: E₀ = mc²
Total energy: E = γmc²
Kinetic energy: K = (γ - 1)mc²
Relativistic momentum: p = γmv
Energy-momentum relation: E² = (pc)² + (mc²)²
The calculator converts every input into SI units first. It then applies the relativistic relation that matches your chosen mode and reports consistent derived values.
When momentum is entered in MeV/c or GeV/c, the script converts that particle-physics unit into SI momentum before solving for total energy, beta, speed, and kinetic energy.
How to Use This Calculator
- Enter a particle label to make the output easier to identify.
- Choose one mode: velocity, momentum, or Lorentz factor.
- Provide the rest mass and select its unit carefully.
- Fill the matching mode input field with your known value.
- Press Calculate Energy to display the results above the form.
- Use the CSV button for spreadsheet work or the PDF button for reports.
- Check beta, gamma, total energy, momentum, and wavelength for consistency.
FAQs
1. What does this calculator compute?
It computes rest energy, total energy, kinetic energy, momentum, beta, gamma, rapidity, and de Broglie wavelength for a particle with nonzero rest mass.
2. Which input mode should I use?
Use velocity when speed is known, momentum when beam momentum is measured, and gamma when the Lorentz factor is already available from analysis or theory.
3. Can I enter mass in particle-physics units?
Yes. The form accepts kg, g, MeV/c², GeV/c², and atomic mass units. The value is converted internally before the relativistic formulas are applied.
4. Why must velocity stay below light speed?
Special relativity requires massive particles to move slower than light. As velocity approaches light speed, gamma rises sharply and the required energy increases without bound.
5. What is the difference between total and kinetic energy?
Total energy includes rest energy and motion-related energy. Kinetic energy is only the extra energy above rest energy, so K = E - E₀.
6. Why is de Broglie wavelength included?
It connects momentum with wave behavior. High-momentum particles have shorter wavelengths, which matters in diffraction, microscopy, scattering, and accelerator beam studies.
7. Does the calculator support photons?
No. This version assumes a positive rest mass. Photons require massless relations, where E = pc and the standard gamma expression for massive particles is not used.
8. When is the momentum mode most useful?
Momentum mode is useful in detector analysis and accelerator work because beamlines, spectrometers, and magnetic bending systems often report momentum directly.