What this calculator does
Relativistic kinetic energy works out kinetic energy of an object moving fast enough that Newtonian mechanics breaks down. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaKE = (γ−1)m₀c², γ = 1/√(1−v²/c²), c = 299,792,458 m/s
The inputs explained
| Field | What to enter |
|---|---|
| Rest mass (kg) | A number, measured in kg. Starts at 1. |
| Speed (m/s) | A number, measured in m/s. Starts at 200000000. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with rest mass
Every other input is held at the calculator’s starting values while rest mass varies. Select any row to load that scenario into the calculator.
How the answer changes with rest mass
| Rest mass (kg) | Relativistic kinetic energy | Lorentz factor γ | Rest energy (m₀c²) |
|---|---|---|---|
| 0.5 | 15,386,001,150,000,000 J | 1.3424 | 44,937,758,940,000,000 J |
| 0.75 | 23,079,001,730,000,000 J | 1.3424 | 67,406,638,410,000,000 J |
| 1 | 30,772,002,300,000,000 J | 1.3424 | 89,875,517,870,000,000 J |
| 1.5 | 46,158,003,450,000,000 J | 1.3424 | 134,813,276,800,000,000 J |
| 2 | 61,544,004,600,000,000 J | 1.3424 | 179,751,035,700,000,000 J |
| 3 | 92,316,006,900,000,000 J | 1.3424 | 269,626,553,600,000,000 J |