Solve relativistic energy, kinetic energy, and momentum together. Check gamma, speed fraction, and equivalence instantly. Built for students, labs, reports, and precise engineering reviews.
Speed ratio: β = v / c
Lorentz factor: γ = 1 / √(1 − β²)
Rest energy: E₀ = mc²
Total relativistic energy: E = γmc²
Relativistic kinetic energy: K = (γ − 1)mc²
Relativistic momentum: p = γmv
Classical kinetic energy: K₍classical₎ = ½mv²
The calculator converts mass and speed into SI units first. It then computes energy and momentum. After that, it converts energy into your selected output unit.
| Rest Mass | Speed | Beta | Gamma | Rest Energy (J) | Kinetic Energy (J) |
|---|---|---|---|---|---|
| 1 kg | 0.10c | 0.1000 | 1.0050 | 8.9876e+16 | 4.5278e+14 |
| 1 kg | 0.50c | 0.5000 | 1.1547 | 8.9876e+16 | 1.3904e+16 |
| 1 kg | 0.90c | 0.9000 | 2.2942 | 8.9876e+16 | 1.1631e+17 |
| 0.001 kg | 0.99c | 0.9900 | 7.0888 | 8.9876e+13 | 5.4724e+14 |
Relativistic energy becomes important when velocity approaches the speed of light. Classical mechanics then loses accuracy. This calculator helps you evaluate total energy, kinetic energy, and momentum with the Lorentz factor. It is useful for physics learning, laboratory checks, simulations, and technical reporting.
The tool starts with rest mass and speed. It converts the inputs into SI units. Next, it calculates beta, gamma, rest energy, total relativistic energy, relativistic kinetic energy, and momentum. It also compares relativistic kinetic energy with the classical value. That comparison shows how quickly the classical estimate fails at high speed.
Special relativity links energy and momentum through Lorentz transformations. The key term is gamma. Gamma rises sharply as velocity moves closer to light speed. That is why kinetic energy does not grow in the simple Newtonian way. Rest energy, written as mc², also shows that mass itself stores enormous energy.
Use beta to see the fraction of light speed. Use gamma to measure relativistic amplification. Rest energy tells you the baseline energy content of mass. Total energy includes rest energy and motion. Relativistic kinetic energy shows the motion contribution only. Momentum is especially helpful in collision and beam calculations. The object count option lets you scale the same case to groups, batches, or particle sets.
This calculator supports classroom exercises, particle motion studies, high speed engineering thought experiments, and report preparation. The CSV download helps with spreadsheets. The PDF output helps with records and sharing. Because the page keeps the layout simple, it is easy to audit each input and verify every result.
Relativistic energy is the total energy of an object moving at high speed. It includes rest energy and motion effects described by special relativity.
Use them when speed becomes a meaningful fraction of light speed. At low speed, classical formulas are usually close enough.
Gamma is the Lorentz factor. It measures how strongly relativistic effects change energy, momentum, and time-related behavior.
Special relativity does not allow objects with rest mass to reach or exceed light speed. Gamma would become undefined at c.
Total energy includes rest energy. Kinetic energy is only the added energy due to motion.
The comparison shows the error in Newtonian estimates. That helps users see when classical mechanics stops being reliable.
Yes. The calculator converts joules into eV, keV, MeV, or GeV, which are common in particle physics.
Momentum is useful for impact studies, particle beam analysis, and conservation calculations. Relativistic momentum grows with gamma and speed.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.