Tool 516 · Translational, rotational & relativistic motion
Kinetic Energy Calculator
Solve classical kinetic energy, quantify uncertainty, switch to special relativity when speed matters, split rolling energy into translation and rotation, or compare several moving objects side by side.
Classical + relativisticShows when ½mv² begins to drift from exact relativistic KE.
Rolling bodiesSolid sphere, shell, disk, hoop, cylinder or custom inertia factor.
Uncertainty-awareOptional first-order σKE from mass and speed uncertainties.
Compare objectsEnergy, momentum, ratios and equivalent drop height.
Solve K = ½mv² for any one variable
Leave exactly one of kinetic energy, mass or speed blank. Optional uncertainty fields propagate first-order measurement uncertainty.
Translational kinetic energy
Optional measurement uncertainty
Uses independent first-order propagation: (σK/K)² ≈ (σm/m)² + (2σv/v)². It is a local linear approximation, not a Monte Carlo uncertainty model.
Special-relativistic kinetic energy
Leave exactly one field blank. Speed must stay below c. The result compares exact K = (γ−1)mc² against classical ½mv².
Rolling without slipping
Leave either total energy or speed blank. Radius does not affect total rolling energy for a fixed κ and center-of-mass speed, but it sets I and angular speed ω = v/r.
General rotational KE helper
Compare moving objects
Label
Mass
Speed