Kinetic Energy Calculator

Kinetic energy: Ec = (1/2)·m·v²

Kinetic energy is what a body holds simply by moving: Ec = (1/2)·m·v², measured in joules, with mass in kg and velocity in m/s. Notice that v shows up squared. Double the speed and the energy goes up four times over, which is the reason a highway-speed crash is so much nastier than one in town. Run the numbers: a 1,500 kg car at 100 km/h (27.8 m/s) packs Ec ≈ 579 kJ ≈ 138 kcal, and a 9 mm bullet (8 g) at 350 m/s carries 490 J. There's also the work-energy theorem, which ties the net work done on a body to its change in kinetic energy: W = ΔEc. Braking distance follows roughly d = v² / (2·μ·g), so it too climbs with the square of the speed.

Applications

You'll find it behind vehicle crash tests (rated in kJ at 50/60 km/h), highway braking distance, forensic ballistics, roller coasters, and free fall, where Ec builds up as potential energy bleeds away. Wind turbines are another case: the kinetic energy of the wind follows (1/2)·ρ·A·v³, which is cubic in wind speed. A small bump in wind speed turns into a huge jump in power.

FAQ

Why does doubling the speed quadruple the energy? The velocity term is squared. So going from 50 to 100 km/h doesn't merely double the crash impact. It makes it four times worse.

Is kinetic energy a vector? No. It's a scalar, always positive or zero, and it has no direction. That sets it apart from momentum, which is a vector, p = m·v.

How does Ec relate to potential energy? When a system is conservative and friction-free, the total mechanical energy stays put: Ec + Ep = constant. Watch a ball drop and you're watching potential energy turn into kinetic energy.