Kinetic energy:
half mass times speed squared

Kinetic energy formula

Kinetic energy is half the mass times the speed squared: KE = 0.5 × m × v². A 1,200 kg car moving at 20 m/s has 0.5 × 1,200 × 400 = 240,000 J, or 240 kJ.

The calculator has two inputs: mass in kg and velocity in m/s. Because the speed is squared, a negative velocity gives the same answer as a positive one, so direction does not matter for energy.

Convert km/h to m/s first

Road speeds are in km/h but the formula needs m/s. Divide km/h by 3.6, because 1 km is 1,000 m and 1 hour is 3,600 s. So 50 km/h is 13.89 m/s, 72 km/h is 20 m/s and 100 km/h is 27.78 m/s.

Skipping this step is the classic mistake. Plugging 50 straight into the formula instead of 13.89 makes the answer about 13 times too large, since 3.6 squared is 12.96.

Why speed matters more than mass

Mass is multiplied once, but speed is squared. Doubling the mass doubles the energy, while doubling the speed multiplies it by four. That is why a car at 100 km/h carries four times the energy of the same car at 50 km/h.

For a 1,000 kg vehicle the pattern is the same at lower speeds: 10 m/s gives 50,000 J, 20 m/s gives 200,000 J and 30 m/s gives 450,000 J. Going from 10 to 30 m/s triples the speed but multiplies the energy by nine.

Check the ratio: 462,963 ÷ 115,741 = 4. This is the reason higher speeds make stopping distances and crash energy rise so steeply. A second example: a 0.145 kg ball thrown at 40 m/s carries 0.5 × 0.145 × 1,600 = 116 J.

Kinetic energy compared with potential energy

Kinetic energy is the energy of motion. Its partner, gravitational potential energy, is the energy of height, found by mass × g × height, with g about 9.81 m/s². A 70 kg person lifted 10 m has about 6,867 J of potential energy.

Kinetic energy also explains why a heavier object at the same speed is harder to stop. A 1,000 kg car and a 2,000 kg van at 20 m/s carry 200,000 J and 400,000 J. The brakes of the van must remove twice as much energy, which is why stopping distances and braking systems are designed around mass and speed together.

In a falling or swinging object the two trade places: potential energy falls as kinetic energy rises. This calculator only does the kinetic part, so the second equation is for working by hand.

Common mistakes

• Using km/h or mph in the formula without converting to m/s.
• Forgetting to square the speed, or squaring the mass instead.
• Using grams instead of kilograms. A 145 g ball is 0.145 kg.
• Expecting the answer in kilojoules. The result is in joules, so divide by 1,000 for kJ.
• Treating energy as if it adds like speed. Energy depends on speed squared.