How to calculate kinetic energy

Kinetic energy is the energy of motion, and it depends far more on speed than on mass. Here is the formula, why squaring the velocity changes everything, worked examples, and how to rearrange it to find speed or mass.

By the Calculator Den team · Updated 2026-10-23

Kinetic energy is the energy an object has because it is moving. A rolling ball, a falling apple, a car on the motorway and a bullet all carry kinetic energy, and the faster and heavier they are, the more they carry. Working it out takes one short formula, but there is one feature of that formula that trips people up and explains a surprising amount about the real world: speed counts far more than mass. A free kinetic energy calculator does the arithmetic, but the method below is what makes the answer make sense.

The kinetic energy formula

The kinetic energy of a moving object is:

KE = ½ × m × v²

Here m is the mass in kilograms, v is the velocity (speed) in metres per second, and the result comes out in joules. The two things people forget are the one half at the front and the square on the velocity. Both matter. A quick worked example: a 2 kg object moving at 3 m/s has a kinetic energy of ½ × 2 × 3² = 0.5 × 2 × 9 = 9 joules.

Why speed matters more than mass

Mass sits in the formula on its own, so doubling the mass doubles the energy. But velocity is squared, so doubling the speed quadruples the energy. That single fact explains a lot. Take a 1,500 kg car. At 20 m/s (about 72 km/h) its kinetic energy is ½ × 1,500 × 20² = 300,000 joules, or 300 kJ. At 40 m/s (about 144 km/h) it is ½ × 1,500 × 40² = 1,200,000 joules, or 1,200 kJ. The speed only doubled, but the energy went up four times.

This is why, with a steady braking force, stopping distance rises roughly with the square of the speed, and why crash forces climb so steeply: all that energy has to go somewhere when the car stops. It is also why a light, fast object like a bullet can carry enormous energy despite weighing almost nothing. When you want to reduce the energy in a moving system, slowing it down beats lightening it, because the speed term is doing the heavy lifting.

Worked examples

A few more, to lock in the method. Always convert speed to metres per second first (divide km/h by 3.6) and mass to kilograms.

• A runner. A 70 kg runner at 5 m/s has ½ × 70 × 5² = ½ × 70 × 25 = 875 joules.
• A cyclist. An 80 kg rider and bike at 36 km/h first convert the speed: 36 ÷ 3.6 = 10 m/s. Then ½ × 80 × 10² = 4,000 joules.
• A dropped ball. A 0.5 kg ball hitting the ground at 8 m/s has ½ × 0.5 × 8² = ½ × 0.5 × 64 = 16 joules.

Rearranging the formula for speed or mass

Sometimes you know the energy and want the speed, or the mass. Rearranging the formula gives you both:

• To find velocity: v = √(2 × KE ÷ m). For the 9-joule, 2 kg object: √(2 × 9 ÷ 2) = √9 = 3 m/s, which matches where we started.
• To find mass: m = 2 × KE ÷ v². For 16 joules at 8 m/s: 2 × 16 ÷ 64 = 0.5 kg.

The square root is the key step when solving for speed, and it is where the energy-to-speed relationship bites again: to double an object's speed you need four times the energy, so going faster gets expensive quickly.

Kinetic energy vs potential energy

Kinetic energy is the energy of motion. Its partner is potential energy, the stored energy an object has because of its position, most commonly gravitational potential energy from height, PE = m × g × h (with g about 9.8 m/s² on Earth). The two trade back and forth. As an object falls, potential energy converts into kinetic energy, and if you ignore air resistance the total stays the same.

A worked example shows the swap. Drop a 2 kg object from 10 m. Its potential energy at the top is 2 × 9.8 × 10 = 196 joules (using g = 9.8 m/s², rounded from 9.81). At the moment it lands, almost all of that has become kinetic energy, so ½ × 2 × v² = 196, which rearranges to v = √(196) = 14 m/s. Notice the mass cancels: the landing speed is v = √(2 × g × h) whatever the object weighs, which is why, ignoring air resistance, a feather and a hammer dropped together hit the ground at the same speed. A pendulum, a roller coaster and a thrown ball all run on this same exchange between height and speed.

Kinetic energy in the real world

The formula is not just an exam exercise. Vehicle safety standards are built around the fact that energy rises with the square of speed, which is why speed limits do so much for crash survivability. Wind turbines and hydro plants harness the energy of moving air and water, though a turbine can only ever capture part of the wind's kinetic energy. In sport, the energy a ball or a punch delivers scales with the square of its speed, which is why technique that adds a little speed adds a lot of impact. Even braking is really an energy problem: the brakes have to turn all of a vehicle's kinetic energy into heat.

Common kinetic energy mistakes

• Forgetting the one half. KE is half of mass times velocity squared, not mass times velocity squared. Leaving out the ½ doubles your answer.
• Not squaring the velocity. The v is squared before you multiply. Squaring at the wrong moment, or not at all, is the most common slip.
• Mixing units. Mass must be in kilograms and speed in metres per second for the answer to be in joules. Convert km/h to m/s by dividing by 3.6, and grams to kilograms by dividing by 1,000.
• Confusing speed and velocity. For kinetic energy only the size of the velocity matters, so direction does not change the result, but the number you square must be the actual speed.

Get the half, the square and the units right and kinetic energy is a one-line calculation. When you want it done instantly, including the km/h to m/s conversion, the free kinetic energy calculator takes mass and velocity and returns the energy in joules, and the force calculator helps with the related F = ma side of motion.