Kinetic Energy Calculator
Calculate kinetic energy KE = ½mv² from mass in kg or lbs and velocity in m/s, km/h, or mph.
Returns energy in Joules, kJ, and ft·lbf for physics problems.
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