How do you calculate kinetic energy?

Multiply half the mass in kilograms by the speed in metres per second squared: KE = ½mv². A 2 kg ball at 3 m/s has ½ × 2 × 9 = 9 J. If the speed is in km/h, divide by 3.6 first; if in mph, multiply by 0.447. The page does the conversions and shows them.

Why is kinetic energy proportional to the square of the speed?

Because energy is force times distance, and the stopping distance at constant deceleration grows with the square of the speed: twice the speed takes twice as long to stop while travelling twice as fast on average, so four times the distance. The work-energy theorem in OpenStax §7.2 derives it directly from Newton's second law.

What is the kinetic energy of a car at 60 mph?

For a 3,300 lb (1,497 kg) car at 60 mph (26.8 m/s), ½ × 1,497 × 26.8² ≈ 538,000 J, or 538 kJ — about 129 kcal. Enter your own car's mass and speed; the page accepts pounds and mph directly.

What is the difference between kinetic energy and momentum?

Momentum is mass × velocity, a vector that is conserved in every collision; kinetic energy is ½mv², a scalar that is conserved only in elastic collisions. Doubling the speed doubles the momentum but quadruples the kinetic energy. The momentum calculator on this site does the other one.

Kinetic Energy Calculator (½mv², any mass and speed unit)

Kinetic energy from mass and speed in kg or lb and m/s, km/h, mph or ft/s, working shown.

Inputs

Mass

0.0011,000,000,000

Mass unit

Speed

01,000,000

Speed unit

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Kinetic energy

250 J

Working (SI): ½ × 5 kg × (10 m/s)² = 250 J
Mass: 5 kg (11.02 lb)
Speed: 10 m/s (36 km/h)
In kJ / kcal: 0.25 kJ / 0.0598 kcal
Doubling the speed: quadruples it: 1,000 J

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What each Kinetic Energy input means

Mass: The moving object's mass. Kilograms or pounds; pounds are treated as mass, not force.
Mass unit: kg or lb. The page converts pounds at 0.45359237 kg each before using the formula.
Speed: Its speed — a positive number, since direction does not affect kinetic energy.
Speed unit: m/s, km/h, mph or ft/s. Everything is converted to m/s first, and the working line shows the converted figure.

Kinetic Energy formula

KE = ½ × m × v² (m in kg, v in m/s, KE in joules) · 1 kJ = 1,000 J · 1 kcal = 4,184 J

KE = \tfrac{1}{2} m v^{2}

Kinetic energy is the energy a moving object has because it is moving — the work it took to bring it up to speed, and the work it can do when it stops. It is half the mass times the speed squared, in joules when the mass is in kilograms and the speed in metres per second, so the page converts pounds, km/h, mph and ft/s to SI first and shows the conversion. The square is the important part: doubling the speed quadruples the energy, which is why a crash at 100 km/h is four times as violent as one at 50 km/h, not twice. Direction does not matter; only how fast. The result is also shown in kilojoules and food calories for a sense of scale — a car on the motorway carries about as much energy as a slice of bread.

Kinetic Energy worked example

A 5 kg mass moving at 10 m/s: ½ × 5 × 10² = ½ × 5 × 100 = 250 J, a quarter of a kilojoule. At 20 m/s the same mass carries 1,000 J, four times as much for double the speed. For comparison, a 1,500 kg car at 100 km/h (27.8 m/s) carries ½ × 1,500 × 27.8² = 578,700 J, about 138 kcal.

More Kinetic Energy examples

A 145 g baseball pitched at 40 m/s (144 km/h, about 90 mph): ½ × 0.145 × 40² = 116 J. A pitch 10% faster carries 21% more energy.

Where the Kinetic Energy calculator can give the wrong answer

This is translational kinetic energy only — the energy of moving from place to place. A spinning wheel or a rolling ball also has rotational kinetic energy (½Iω²), which is not included.
The formula is Newtonian and is accurate for everyday speeds. Above roughly a tenth of the speed of light, relativistic kinetic energy takes over and ½mv² understates the true value.
Speed, not velocity: the page takes a non-negative speed, since squaring removes the sign anyway. Two cars approaching each other at 50 km/h each have the same kinetic energy in the road's frame, and the collision energy is a different question involving their relative speed and how they stop.
Mass in pounds is treated as mass (pound-mass), converted at 0.45359237 kg per lb, not as pound-force.
Food calories are given for scale only: a kilocalorie is 4,184 J of heat, and a body does not turn motion into food energy or the reverse at 100%.

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Kinetic Energy reference table

Kinetic energy of a 1,500 kg car at different speeds
Speed	Kinetic energy	Compared with 50 km/h
30 km/h	52,083 J	0.36×
50 km/h	144,676 J	1×
80 km/h	370,370 J	2.56×
100 km/h	578,704 J	4×
120 km/h	833,333 J	5.76×

Source: Arithmetic: KE = ½mv² with v = km/h ÷ 3.6 (OpenStax College Physics 2e, §7.2)

Kinetic Energy FAQ

: Multiply half the mass in kilograms by the speed in metres per second squared: KE = ½mv². A 2 kg ball at 3 m/s has ½ × 2 × 9 = 9 J. If the speed is in km/h, divide by 3.6 first; if in mph, multiply by 0.447. The page does the conversions and shows them.
: Because energy is force times distance, and the stopping distance at constant deceleration grows with the square of the speed: twice the speed takes twice as long to stop while travelling twice as fast on average, so four times the distance. The work-energy theorem in OpenStax §7.2 derives it directly from Newton's second law.
: For a 3,300 lb (1,497 kg) car at 60 mph (26.8 m/s), ½ × 1,497 × 26.8² ≈ 538,000 J, or 538 kJ — about 129 kcal. Enter your own car's mass and speed; the page accepts pounds and mph directly.
: Momentum is mass × velocity, a vector that is conserved in every collision; kinetic energy is ½mv², a scalar that is conserved only in elastic collisions. Doubling the speed doubles the momentum but quadruples the kinetic energy. The momentum calculator on this site does the other one.