How to use the Kinetic Energy Calculator
- Enter the mass in kilograms.
- Enter the velocity in metres per second — divide km/h by 3.6, or multiply mph by 0.447.
- Read the kinetic energy in joules and kilojoules.
- Compare the momentum figure, which scales linearly with speed rather than quadratically.
- Use the equivalent drop height to translate an abstract energy figure into something intuitive.
How the calculation works
Kinetic energy is the work needed to accelerate a body from rest to its current speed, and it scales with the square of velocity. That square is the single most important fact in road safety: doubling speed quadruples the energy that brakes, crumple zones or a barrier must absorb, which is why stopping distances grow so much faster than speed limits suggest.
Momentum, by contrast, scales linearly with velocity. The two quantities answer different questions: momentum governs what happens in a collision through impulse and conservation, while energy governs how much damage is done and how much braking distance is required. A heavy slow object and a light fast one can share momentum while differing hugely in energy.
The formula ½mv² is the low-speed limit of the relativistic expression and is accurate to better than 1% below about 10% of the speed of light. Above that the Lorentz factor becomes significant and the classical result understates the true energy — relevant in particle physics and irrelevant for vehicles, projectiles and machinery.
KE = ½mv²; momentum p = mv; equivalent drop height h = KE ÷ (m × g)Source: Halliday, Resnick & Walker, Fundamentals of Physics, 11th edition; NIST Special Publication 811 unit conventions.
Worked example
Comparing a 1,500 kg car at 50 km/h and at 100 km/h.
- 50 km/h = 13.89 m/s: KE = 0.5 × 1500 × 13.89² = 144,700 J.
- 100 km/h = 27.78 m/s: KE = 0.5 × 1500 × 27.78² = 578,800 J.
- The ratio is exactly 4, not 2.
- The drop-height equivalent at 100 km/h is 578,800 ÷ (1500 × 9.807) = 39.3 m.
Doubling speed quadruples the energy: a 100 km/h impact carries as much energy as dropping the car from a 13-storey building.
Frequently asked questions
Why does energy scale with the square of speed?+
Because work is force times distance, and both the force needed and the distance covered during acceleration grow with speed. Integrating gives the v² term.
What is the difference between energy and momentum?+
Momentum is mv and is conserved in every collision. Kinetic energy is ½mv² and is only conserved in perfectly elastic collisions.
How do I convert km/h to m/s?+
Divide by 3.6. For mph, multiply by 0.44704.
Does this apply to rotating objects?+
Rotation adds ½Iω² on top of the translational term. A rolling wheel therefore carries more energy than this calculator alone reports.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.