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Kinetic energy is half the mass times velocity squared. Doubling the speed quadruples the energy, while doubling the mass only doubles it, which is why speed matters so much in crashes and braking distances.
Kinetic energy is the energy of motion. The definition is simple: it is the work needed to speed an object up from rest to its current speed. The formula is kinetic energy equals 0.5 times mass times velocity squared. Mass must be in kilograms and velocity in metres per second, and the answer comes out in joules. One joule equals one kilogram metre squared per second squared. For larger answers, convert with kinetic energy conversion: divide joules by 1000 to get kilojoules, and remember that one joule is about 0.239 calories and about 0.738 foot pounds.
Velocity squared is the reason speed matters so much. Double the mass and the energy doubles. Double the speed and the energy quadruples, because 2 squared is 4. Triple the speed and the energy is 9 times larger. This is also why braking distance grows so fast: a car at 60 miles per hour carries about 4 times the kinetic energy of the same car at 30 miles per hour, so it needs much more distance and much more braking work to stop. The work energy theorem says the same thing in another form: the net work done on an object equals its change in kinetic energy.
A 10 kilogram object moving at 5 metres per second has 0.5 times 10 times 25, which is 125 joules. A baseball of 0.145 kilograms at 40 metres per second has 0.5 times 0.145 times 1600, which is 116 joules. A running person of 70 kilograms at 5 metres per second has 875 joules. The kinetic energy of a car is far larger: a 1500 kilogram car at 20 metres per second has 0.5 times 1500 times 400, which is 300000 joules, or 300 kilojoules. Try these numbers in the calculator and check that the same inputs give the same answers.
Kinetic energy vs potential energy is a common comparison. Kinetic energy depends on motion, while potential energy depends on position, such as height above the ground. A ball held high has potential energy and no kinetic energy. As it falls, potential energy turns into kinetic energy, and just before it lands almost all of it is kinetic energy. A pendulum shows the same exchange: it is fastest at the bottom of its swing, where kinetic energy is highest, and slowest at the ends, where potential energy is highest.
Kinetic energy vs momentum confuses many learners, because both use mass and velocity. Momentum is mass times velocity, it is a vector with a direction, and it grows in step with velocity. Kinetic energy is a scalar with no direction, and it grows with velocity squared. From momentum, kinetic energy can also be written as momentum squared divided by twice the mass. A heavy slow object and a light fast object can share the same momentum but have very different kinetic energies.
Rotational kinetic energy is the energy of a spinning object. Its formula is 0.5 times moment of inertia times angular velocity squared, where moment of inertia depends on how the mass is spread around the axis. A flywheel, a spinning wheel, and a figure skater pulling in their arms all show rotational kinetic energy. This calculator covers straight line motion only, so for a spinning object use the rotational formula with the correct moment of inertia instead of the mass and speed used here.
The most common mistakes are easy to avoid. First, square the velocity before multiplying, or the answer will be far too small. Second, convert mass to kilograms and velocity to metres per second first: weight in newtons is not mass, and miles per hour is not metres per second. Third, do not drop the 0.5 factor. Fourth, remember that kinetic energy is never negative, because velocity is squared, so a negative velocity still gives a positive energy. Fifth, the simple formula ignores friction and air resistance, so a real object loses some energy to heat and drag.
Enter mass in kilograms and velocity in metres per second, then read the energy in joules and kilojoules. To see the effect of speed, double the velocity and watch the answer quadruple. To check a car example, enter 1500 kilograms and 20 metres per second and confirm 300 kilojoules. This page gives estimates from the ideal formula for learning and checking homework, not professional engineering advice for safety design.
Kinetic energy is the energy an object has because it is moving. It depends on the mass of the object and on how fast it is moving, and it is measured in joules.
Kinetic energy equals 0.5 times mass times velocity squared. Mass is in kilograms, velocity is in metres per second, and the result is in joules.
First convert mass to kilograms and velocity to metres per second. Then square the velocity, multiply by the mass, and halve the result. For 10 kilograms at 5 metres per second: 5 squared is 25, 10 times 25 is 250, and half of 250 is 125 joules.
Velocity is squared because of how work builds up as an object speeds up. Doubling speed therefore quadruples kinetic energy, and tripling speed makes it 9 times larger.
The standard unit is the joule. Larger energies are often given in kilojoules, where 1000 joules equal 1 kilojoule. Other units include calories, watt hours, foot pounds, and electronvolts.
Kinetic energy comes from motion, while potential energy comes from position, such as height. A falling object loses potential energy and gains kinetic energy, and a pendulum swaps between the two on every swing.
No. Kinetic energy is always zero or positive, because velocity is squared in the formula. An object at rest has zero kinetic energy, and a moving object has positive kinetic energy whatever its direction.
Momentum is mass times velocity and has a direction, while kinetic energy is 0.5 times mass times velocity squared and has no direction. Kinetic energy can also be written as momentum squared divided by twice the mass.
Rotational kinetic energy is the energy of a spinning object, given by 0.5 times moment of inertia times angular velocity squared. It applies to wheels, flywheels, and spinning skaters, and it is separate from the straight line formula on this page.
No. The ideal formula assumes no friction and no air drag. In real life some kinetic energy is lost as heat and sound, so a real stopping distance is longer than a frictionless estimate.