Kinetic energy
Translational energy in the chosen reference frame.
Physics · Mechanics · Motion & Energy
Kinetic energy calculator
Find translational kinetic energy from mass and speed, or solve for mass or speed from a known energy.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Mass
Mass required for the specified energy and speed.
Speed
Speed magnitude for the specified energy and mass.
Relation and numerical substitution
Eₖ = ½mv²—
Constant positive mass; translation in a specified reference frame. Classical mechanics at speeds far below the speed of light.
01Formulas and symbols
Formulas used
Eₖ
Eₖ = ½mv²Translation energy depends on mass and the square of speed.m
m = 2Eₖ/v²Solve for a positive mass using a nonzero speed.v
v = √(2Eₖ/m)Solve for speed magnitude, not its direction.02Assumptions and limits
Scope of validity
- Constant positive mass; translation in a specified reference frame.
- Classical mechanics at speeds far below the speed of light.
03Validation example
Reference numerical case
- Given m = 80 kg and v = 36 km/h, find kinetic energy. Convert 36 km/h = 10 m/s.
- Eₖ = ½ × 80 × 10² = 4000 J = 4 kJ. The inverse modes return 80 kg or 10 m/s.
04References
Technical references
FAQ
Why does doubling speed quadruple kinetic energy?
Because kinetic energy is proportional to the square of speed: Eₖ = ½mv². At fixed mass, replacing v by 2v multiplies the energy by 2² = 4.
Does kinetic energy depend on the direction of velocity?
No. Translational kinetic energy depends on the speed magnitude v, not its direction. It does depend on the chosen reference frame because the measured speed can change between observers.
05How it works
At a fixed speed, twice the mass carries twice the kinetic energy. At a fixed mass, doubling speed multiplies the energy by four: 80 kg at 20 m/s carries 16 kJ.
Energy depends on the chosen reference frame. A moving object can be at rest relative to a passenger travelling beside it.
06Limits of the model
This model excludes rotational and internal energy. Relativistic motion requires a different relation.
Zero speed gives zero energy, but energy and zero speed cannot determine a unique mass.
07Common mistakes
Convert km/h to m/s before squaring speed; using 36 as m/s instead of 10 overstates energy by a factor of 12.96.
Momentum is mv; kinetic energy is ½mv². They have different units and cannot be interchanged.