Calculator
Example data table
| Case | Input summary | Momentum | Total energy | Notes |
|---|---|---|---|---|
| Relativistic particle | m = 0.01 kg, v = 0.80c | 3.997e+06 kg·m/s | 1.498e+15 J | Strong deviation from classical kinetic energy. |
| Momentum-driven input | m = 0.01 kg, p = 5.000e+06 kg·m/s | 5.000e+06 kg·m/s | 1.748e+15 J | Useful when experiments report momentum directly. |
| Relation solver | m = 0.01 kg, p = 5.000e+06 kg·m/s | 5.000e+06 kg·m/s | 1.748e+15 J | Matches the invariant energy relation. |
| Green-light photon | λ = 550 nm | 1.205e-27 kg·m/s | 3.612e-19 J | Photon calculations use E = hf and p = E/c. |
Formula used
Relativistic momentum: p = γmv
Lorentz factor: γ = 1 / √(1 − v²/c²)
Total energy: E = γmc²
Kinetic energy: K = E − mc²
Energy–momentum relation: E² = (pc)² + (mc²)²
Photon energy: E = hf
Photon momentum: p = E / c = h / λ
de Broglie wavelength: λ = h / p
The calculator uses c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, and the exact electron charge for eV conversion.
How to use this calculator
- Select the calculation mode that matches your known values.
- Enter inputs in the visible fields only. Hidden fields are ignored.
- Choose a display precision for cleaner scientific notation or detailed decimals.
- Press Calculate to show the result block above the form.
- Review the table, inspect the Plotly graph, and download CSV or PDF reports.
- Use the example data table to validate your own test cases.
FAQs
1. When should I choose relativistic mode?
Choose relativistic mode whenever velocity is a noticeable fraction of light speed, or when high-energy experiments report momentum instead of ordinary speed.
2. Why are classical and relativistic kinetic energies different?
Classical kinetic energy assumes low speeds. Near light speed, the Lorentz factor grows rapidly, so relativistic kinetic energy rises much faster.
3. Can this page solve the invariant energy relation directly?
Yes. The relation solver can solve for total energy, momentum, or rest mass from the other known quantities.
4. Does the photon mode require mass input?
No. Photon mode uses frequency or wavelength. It then computes photon energy, momentum, equivalent mass, angular frequency, and wavenumber.
5. What units are used internally?
All core calculations use SI units internally. The relation solver also accepts common electron-volt energy units for convenience.
6. Why is scientific notation shown?
Energy and wavelength values can become extremely large or tiny. Scientific notation keeps results readable without losing scale information.
7. What does the chart represent?
The chart changes by mode. It plots how energy varies with velocity, momentum, or frequency, and marks the calculated point.
8. Can I export the results for reports?
Yes. Use the CSV button for spreadsheet work and the PDF button for quick printable documentation of the current result table.