Kinetic energy is the energy an object has by virtue of being in motion: KE = ½ × m × v², in joules when mass is in kilograms and velocity in m/s. The Toolenza calculator returns kinetic energy and also momentum (p = m × v) so you get the two motion quantities together.

Why the v² matters more than you'd think

The quadratic dependence on velocity is the whole story. Doubling the speed quadruples the energy. That's why:

• A car at 60 mph carries 4× the kinetic energy of the same car at 30 mph, not 2× — which is why stopping distances grow super-linearly with speed and why highway crashes are categorically worse than parking-lot crashes.
• An object falling from twice the height hits the ground with √2 times the velocity but 2× the kinetic energy (since the energy gained equals the work done by gravity, which is linear in height).
• A bullet's stopping power is dominated by velocity, not mass. A 5g bullet at 900 m/s carries ~2,025 J — about 4× the energy of a 10g bullet at 450 m/s (1,012 J) even though the bullets have the same momentum.

Worked example

A 1,500 kg car at 30 m/s (≈ 67 mph): KE = ½ × 1500 × 30² = 675,000 J = 675 kJ. That's the energy that has to go somewhere when the car stops. Distributed over a 30-metre braking distance, that's a 22,500 N average decelerating force — about 1.5× the car's weight. Distributed over a 1-metre crumple zone in a crash, it's 675,000 N. The numbers explain why crumple zones, not seat belts, do most of the survival work in a collision.

Limits

The formula assumes constant mass, non-relativistic speeds, and a point mass or rigid body. For rotating objects you add the rotational term ½ × I × ω² (where I is moment of inertia and ω is angular velocity). For relativistic speeds (significant fraction of c), use γmc² − mc². For variable mass (rockets, dissolving particles), you need the full energy-balance equation.