What is kinetic energy?

Kinetic energy is the energy an object possesses because of its motion. Any moving object has it, and bringing the object to rest releases exactly that much energy — which is why a moving car must dissipate all of its kinetic energy as heat in the brakes before it can stop. The formula is KE = ½mv², measured in joules, and it depends on only two things: how heavy the object is and how fast it is going.

Why does doubling the speed quadruple the energy?

Because the speed term is squared. If you double v, then v² becomes four times larger, and since energy is proportional to v², the energy quadruples. Triple the speed and you get nine times the energy; halve it and you keep only a quarter. This is why speed limits matter so much: a car at 60 km/h carries four times the energy it had at 30 km/h, and all of that extra energy must go somewhere in a collision.

How do I calculate kinetic energy?

Convert mass to kilograms and speed to metres per second, square the speed, multiply by the mass and halve it. A 1,500 kg car at 60 mph is 26.8224 m/s, so v² is 719.44, and KE = ½ × 1,500 × 719.44 = 539,581 joules, about 540 kJ. The commonest error is forgetting to square the speed or leaving it in km/h — either mistake throws the answer out by a large factor.

A joule is the SI unit of energy, equal to 1 kg·m²/s². One joule is roughly the energy of a tennis ball dropped about 20 centimetres, or of an apple falling one metre. A food Calorie is 4,184 joules, and a kilowatt-hour is 3.6 million joules. Because everyday kinetic energies span an enormous range — from a fraction of a joule for a falling coin to millions for a moving truck — this page also plots your answer on a logarithmic scale.

What is the difference between kinetic energy and momentum?

Both describe motion but they behave very differently. Momentum is mass times velocity, p = mv, so it grows in direct proportion to speed and it is a vector with direction. Kinetic energy is ½mv², grows with the square of speed, and is a scalar with no direction. In a collision, momentum is always conserved, whereas kinetic energy is only conserved in a perfectly elastic collision — in real crashes much of it is converted into deformation, sound and heat.

How high could an object rise with its kinetic energy?

Fired straight upward and ignoring air resistance, it would reach h = v² ÷ 2g. Notice that mass cancels out completely, so the height depends only on speed — a bullet and a truck travelling at the same speed would coast to exactly the same height. At 10 m/s that is about 5.1 metres, and at 100 m/s about 510 metres. It is the same physics as the free-fall calculation, simply run in reverse.

Why does a bullet carry so much energy despite being tiny?

Because speed is squared and mass is not. A 4 gram bullet at 900 m/s has KE = ½ × 0.004 × 810,000 = 1,620 joules. An 80 kg cyclist at 8 m/s has ½ × 80 × 64 = 2,560 joules. The cyclist is 20,000 times heavier yet carries less than twice the energy, because the bullet is over a hundred times faster and that advantage gets squared. It is the clearest demonstration that speed dominates the equation.

How does kinetic energy relate to braking distance?

Under steady braking force, stopping distance is proportional to kinetic energy and therefore to the square of speed. The work-energy theorem says the braking force multiplied by the distance must equal the kinetic energy removed, so doubling the speed quadruples the distance needed. That is why a modest increase in speed lengthens stopping distance far more than most drivers expect, and why the last few metres before an impact matter so much.

Does the formula work at very high speeds?

½mv² is an approximation that is excellent for anything up to a few percent of the speed of light, which covers every practical situation on Earth. Beyond that, relativity takes over and the correct expression is KE = (γ − 1)mc², where γ grows without limit as speed approaches c. The classical formula starts to understate the true energy noticeably around a tenth of light speed, and particle accelerators must use the relativistic form throughout.

Kinetic Energy Calculator (KE = ½mv²)

Calculate kinetic energy, mass or speed from KE = ½mv² — the energy an object carries purely because it is moving. Enter any two of the three and this calculator returns the third, converts it into joules, kilojoules, food Calories and foot-pounds, and shows you what that energy actually amounts to....

KE = ½ m v²

SOLVE FOR

MASS

SPEED

EVERYDAY EXAMPLES

KINETIC ENERGY

539,580.9 J

KILOJOULES

539.581

FOOD CALORIES

128.963

FOOT-POUNDS

397,974.4

Mass

1,500.000 kg

Speed

26.822 m/s

Energy

539,580.86 J

At double speed

2,158,323.4 J

At half speed

134,895.2 J

Momentum (mv)

40,233.60 kg·m/s

STEPS

Convert to SI: mass = 1,500.0000 kg, speed = 26.8224 m/s

Square the speed: v² = 26.8224² = 719.4411

KE = ½ × 1,500.0000 × 719.4411 = 539,580.8563 J

WHY SPEED MATTERS MORE THAN MASS

HOW BIG IS THIS ENERGY?

WHAT THAT ENERGY COULD DO

Lift itself straight up

36.68 m

Food Calories

128.9629 kcal

Run a 60 W bulb for

8,993.01 s

Equivalent TNT

128.9629 g

The rise height is v² ÷ 2g — the same for every mass, which is exactly why a bullet and a truck at the same speed would coast to the same height.

Live simulation · updates as you type

Created with❤️byeaglecalculator.com

HOW TO USE

1
Choose what to find with the SOLVE FOR buttons: Energy, Mass or Speed. The fields change to ask for whichever two quantities the calculation needs.
2
Enter your values and pick units beside each field. Mass in kilograms, grams, tonnes or pounds; speed in m/s, km/h, mph or ft/s; energy in joules, kilojoules, megajoules, food Calories or kilowatt-hours. Everything converts to SI before the maths runs.
3
Read the answer in the black box with three alternative units below it, then check the key-facts grid — it also shows what the energy would be at double and half the speed, so the v² effect is right there in numbers.
4
Watch the simulation on the right. The ramp shows energy falling behind speed and then overtaking it, the ladder compares half, actual and double speed as 1 : 4 : 16, and the logarithmic scale places your answer among everyday and extreme examples.

THE FORMULAS

Kinetic energyKE = ½ m v²

Solve for massm = 2KE ÷ v²

Solve for speedv = √(2KE ÷ m)

One joule1 J = 1 kg·m²/s²

Work–energy theoremW = ΔKE

From momentumKE = p² ÷ 2m

Rise heighth = v² ÷ 2g

Food Calorie1 kcal = 4,184 J

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Last updated: July 28, 2026 · Formula verified · Eagle-eyed accuracy for every calculation.