Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity using KE = ½mv².
Supports SI (Joules) and Imperial (ft·lbf) units.
Kinetic energy is the energy an object has due to its motion. Potential energy is stored energy due to position in a gravitational field. Together, they form the basis of mechanical energy and conservation of energy principles.
The Formulas:
Kinetic Energy: KE = 0.5 × m × v^2
Potential Energy (gravitational): PE = m × g × h
Where:
- m = mass (kg)
- v = velocity (m/s)
- g = gravitational acceleration = 9.81 m/s² (Earth surface)
- h = height above reference point (m)
Conservation of Energy:
In a frictionless system: KE + PE = constant
At the top of a drop: KE = 0, PE = mgh At the bottom: PE = 0, KE = 0.5mv² → so v = sqrt(2gh)
Worked Example:
A 2 kg ball is dropped from a height of 10 m.
PE at top = 2 × 9.81 × 10 = 196.2 J
KE at impact (all PE converted): 196.2 J
Impact velocity: v = sqrt(2 × 196.2 / 2) = sqrt(196.2) = 14 m/s
Energy Comparison Reference:
| Event | Energy |
|---|---|
| Lifting a 1 kg book 1 m | 9.81 J |
| 80 kg person running at 5 m/s | 1,000 J (1 kJ) |
| 1,400 kg car at 100 km/h | 540,000 J (540 kJ) |
| Lightning bolt | ~1,000,000,000 J (1 GJ) |
Rotational Kinetic Energy:
KE_rot = 0.5 × I × ω²
Where I = moment of inertia (depends on object shape) and ω = angular velocity (rad/s)
Practical Tips:
- KE scales with velocity squared — doubling speed quadruples kinetic energy (explains why car crashes at 100 km/h are 4× worse than at 50 km/h)
- Energy is conserved in ideal systems but heat and sound losses occur in real-world scenarios