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Science

Kinetic Energy Calculator (KE = ½ m v²)

Enter a mass and speed to get the kinetic energy (KE) — the energy a moving object carries, equal to ½ × mass × speed². The result is shown in joules (J), kilojoules (kJ), kilocalories (food calories), foot-pounds force (ft·lbf) and watt-hours (Wh), so you can compare across cars, bullets, athletes and appliance energy use.

Kinetic energy (KE)

Other units

Kilojoules
Kilocalories (food calories)
Foot-pounds force
Watt-hours

1 Wh = 3600 J — handy for comparing against household appliance energy use.

Formula

KE = ½ · m · v² (m in kg, v in m/s, result in J = kg·m²/s²)

Kinetic energy scales with the square of speed — double the speed and energy quadruples. Inputs are normalised to kg and m/s before the formula is applied.

Formula

KE = ½ · m · v² // m in kg, v in m/s, KE in J (kg·m²/s²) 1 J = 1 N·m = 1 kg·m²/s² 1 kJ = 1000 J 1 kcal = 4184 J // food calorie 1 ft·lbf ≈ 1.3558 J 1 Wh = 3600 J

Frequently asked

How much kinetic energy does a 1500 kg car at 100 km/h carry?

100 km/h ≈ 27.78 m/s. Plugging in: KE = ½ × 1500 × 27.78² ≈ 578 700 J ≈ 578.7 kJ ≈ 138.3 kcal. In a crash, the car has to dissipate roughly a quarter of the energy in a Big Mac (≈ 550 kcal). Bump the speed to 120 km/h (33.33 m/s) and KE jumps to ≈ 833 kJ — a 44 % increase, not 20 %.

If I double the speed, by how much does the kinetic energy go up?

It quadruples. The v in KE = ½ m v² is squared, so v → 2v gives 4× the energy, and v → 3v gives 9×. That's why crash forces, braking distance and running injury risk all scale with the square of speed — a small bump in speed produces a much bigger jump in energy.

How do joules and food calories (kcal) relate?

One food calorie equals 4184 joules (the international thermochemical definition). So a 100 kcal apple holds 418 400 J of chemical energy — roughly the kinetic energy of throwing your own 70 kg body at 109 km/h. The "kcal" row in this calculator just divides joules by 4184 so you can compare against food labels at a glance.

Why does kinetic energy turn into heat, sound and deformation?

Conservation of energy. When a moving object is brought to rest (a car hitting a wall, a bullet stopping in wood), its kinetic energy doesn't vanish — it converts into permanent deformation of metal, friction heat, sound waves and a tiny bit of light. The higher the kinetic energy, the more "somewhere" you need for it to go before it reaches the occupants. That's the entire reason crumple zones and airbags exist.

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