How this instrument works
Kinetic energy is the energy an object has because it is moving — precisely the work something had to do to bring it from rest up to speed, and exactly what the object hands back when something stops it. The formula KE = m·v² ⁄ 2 says mass and speed do not contribute equally: mass enters once, speed enters twice. A 6,000 kg truck at 30 km/h and a 1,500 kg car at 60 km/h carry exactly the same energy, even though the truck weighs four times as much.
That squared term is the whole story of why speed is dangerous. Doubling your speed quadruples the energy the brakes must dissipate; tripling it gives nine times. This is not an approximation or a safety slogan — it falls straight out of the algebra, and it is why stopping distances in driving manuals grow so much faster than the speeds do.
The result arrives in joules, the SI unit of energy: one joule is one kilogram-metre-squared per second-squared, which is why the instrument converts your inputs to kilograms and metres per second before computing. The unit menu on the output line converts to kilojoules, watt-hours, or kilocalories — handy for comparing a moving car with a battery or a snack.
- Set the Mass field — grams, kilograms, tonnes, or pounds from the unit menu. The default 1500 kg is a mid-size car.
- Set the Speed field in m/s, km/h, or mph. Whatever you pick is converted to metres per second before the squaring.
- Read the Kinetic energy line in joules, or flip its unit to kJ, Wh, or kcal for a friendlier scale.
- Halve the speed and watch the result fall to a quarter — the square in the formula, demonstrated live.
Worked example — a 1500 kg car at 100 km/h
Take a mid-size car: mass 1500 kg, speed 27.78 m/s — which is 100.0 km/h, or 62.1 mph. Square the speed first: 27.78² = 771.7284. Multiply by the mass: 1500 × 771.7284 = 1,157,592.6. Halve it: KE = 578,796 J. Call it 579 kJ — or, from the unit menu, 161 watt-hours or 138 kilocalories, a little more than a large banana.
All 579 kJ must go somewhere when the car stops: into hot brake discs in the good case, into crumpled metal in the bad one. At 50 km/h the same car carries a quarter of that figure — about 145 kJ — which is the quiet arithmetic behind urban speed limits.
Questions
Why is speed squared but mass is not?
Because kinetic energy equals the work done accelerating the object, and work is force times distance. A faster object needs the force applied over a longer distance to reach its speed — speed raises both the rate of gain and the distance covered, so it counts twice. Mass only scales the force required, so it counts once. The practical consequence: a 10% speed increase means 21% more energy to get rid of.
Is kinetic energy the same as momentum?
No. Momentum is m·v — linear in speed and directional; it governs collisions and recoil. Kinetic energy is m·v² ⁄ 2 — a scalar, always positive, and it governs damage, braking, and heating. A 10,000 kg truck rolling at 1 m/s and a 10 kg shell flying at 1,000 m/s have identical momentum, but the shell carries a thousand times the energy.
Do I have to convert my units to kilograms and metres per second first?
No — enter values in any unit the menus offer. The instrument converts mass to kilograms and speed to metres per second, computes joules, then presents the result in whichever unit you select, with kJ, Wh, and kcal on the output menu. The one thing it will not do is guess: a figure typed as pounds while the menu reads kilograms is simply a different mass.
How does a bullet compare with a car?
The car wins by a wide margin. A 9 mm bullet of 8 g at 360 m/s carries about 518 J; the 1500 kg car at 100 km/h in the worked example carries 578,796 J — over a thousand times more. The bullet is dangerous because its energy is delivered into a few square millimetres; the car spreads a far larger total across bumpers, crumple zones, and time.
Is the formula still valid at very high speeds?
Up to a few percent of light speed, effectively yes. Classical KE = m·v² ⁄ 2 is the low-speed limit of the relativistic expression; at 10% of light speed it understates the true value by under 1%, and at driving, orbital, or even interplanetary speeds the error is negligible. For particle physics, switch to (γ−1)mc².
Can kinetic energy ever be negative?
No. Mass is positive and the speed term is squared, so the result is zero for anything at rest and positive for anything moving — direction does not matter, and reversing counts the same as advancing. What can be negative is a change in kinetic energy: brakes, friction, and collisions all remove it, turning it into heat and deformation.