Kinetic energy
KE = ½mv²
Translational kinetic energy in classical mechanics.
Kinetic Energy Calculator
Calculate translational kinetic energy and momentum from object mass and speed.
Access: Free to use, no installation, and No account required.
Inputs
This is classical translational kinetic energy. Relativistic effects and rotational kinetic energy are not included.
Results
Kinetic energy scales with velocity squared
The classical relation is KE = ½mv². Doubling mass doubles energy, while doubling speed quadruples energy.
Engineering reference
Kinetic Energy Calculator: background and worked detail
Use the Kinetic Energy Calculator to calculate classical translational kinetic energy, momentum, and specific kinetic energy from mass and speed.
Kinetic energy and momentum
Momentum
p = mv
Linear momentum scales directly with both mass and velocity.
Specific kinetic energy
KE/m = ½v²
Energy per unit mass depends only on speed in the classical model.
1,000 kg vehicle at 20 m/s
Use mass 1,000 kg and speed 20 m/s.
- KE = 0.5 × 1,000 × 20² = 200,000 J.
- Momentum magnitude is 20,000 kg·m/s.
- Specific kinetic energy is 200 J/kg.
Result: Doubling the speed to 40 m/s would raise kinetic energy to 800 kJ while only doubling momentum.
Engineering theory and interpretation
Classical kinetic energy is one half mass times speed squared, while momentum is mass times velocity. The squared speed dependence means small increases in speed can produce large increases in energy.
The model is non-relativistic and treats the object as a point mass for translational motion. Rotational kinetic energy and relativistic corrections are not included.
Assumptions and model boundaries
Assumptions
- Classical, non-relativistic translational mechanics.
- Mass is constant.
- Only speed magnitude is used for the displayed energy.
Limitations
- Does not include rotational energy or relativistic corrections.
- Momentum direction is not represented because the focused input uses scalar speed.
Kinetic Energy Calculator FAQ
Why does kinetic energy rise faster than momentum?
Momentum is proportional to v, while kinetic energy is proportional to v².
When do I need relativistic kinetic energy?
When speed becomes a significant fraction of the speed of light, classical KE = ½mv² loses accuracy.
Does this include rotational energy?
No. A rolling wheel or rotating machine can also store ½Iω² rotational kinetic energy.
Validation checks
Zero speed
Case: Set speed to 0.
Expected: Kinetic energy and momentum should both be zero.
Speed scaling
Case: Double speed with mass unchanged.
Expected: Momentum should double while kinetic energy quadruples.
Where this calculation comes from
Shared with the Mechanics Workbench.
Open the source workbench →Read calculation and source methodology →