Kinetic Energy Calculator - Joules, kJ, kWh and kcal

Kinetic energy in four numbers

Twice the speed is not twice the energy. It is four times, and that one fact explains more about road safety, ballistics and braking than any other line in mechanics. This calculator takes a mass and a speed and returns the energy of the motion, or works backwards from an energy to the mass or the speed that would carry it. All four numbers below describe the same ordinary car.

135 kJ

a 1,400 kg car at 50 km/h, 31 mph

4×

what doubling the speed costs

9.84 m

the drop that matches it

0.0375 kWh

the same energy, bought as electricity

Why the square is the whole story

The formula is Ek = ½mv², and the asymmetry between its two inputs is the point. Mass enters once: put twice as much matter in motion at the same speed and you have twice the energy. Speed enters twice, so it compounds against itself. Going twice as fast is not a doubling of anything the body carries, it is a quadrupling, and going three times as fast is a ninefold increase.

This is why speed limits are argued over so much more than weight limits. A 1,400 kg car at 50 km/h, 31 mph, carries 135.03 kJ. Load it up to 1,900 kg and it carries 183.26 kJ, about thirty-six percent more. Leave it empty but drive at 100 km/h, 62 mph, and it carries 540.12 kJ, four times as much. The extra passengers are a rounding error next to the extra fifty kilometers an hour, thirty-one miles an hour.

The same square explains why the last increment of speed always costs the most. Going from 30 to 50 km/h, 19 to 31 mph, adds 86.42 kJ. Going from 110 to 130 km/h, 68 to 81 mph, exactly the same twenty kilometers an hour, adds 259.26 kJ, three times as much again. Nothing about the car changed. Only where on the curve the twenty was added.

One car, six speeds

Every row below is the same 1,400 kg. The only thing that moves is the speedometer, and the last column is the height that body would have to be dropped from to arrive with the energy it already has at that speed.

Speed	In mph	Kinetic energy	Against 50 km/h	Equivalent drop
30 km/h	18.6	48.61 kJ	0.36×	3.54 m
50 km/h	31.1	135.03 kJ	1.00×	9.84 m
70 km/h	43.5	264.66 kJ	1.96×	19.28 m
90 km/h	55.9	437.50 kJ	3.24×	31.87 m
110 km/h	68.4	653.55 kJ	4.84×	47.60 m
130 km/h	80.8	912.81 kJ	6.76×	66.49 m

The third column is just the speed ratio multiplied by itself, which you can check on any row: 130 over 50 is 2.6, and 2.6 squared is 6.76. The fourth is worth reading twice. Taking a floor as roughly 3.3 m, a crash into something immovable at 50 km/h is a fall from the third floor. At 130 km/h, 81 mph, it is a fall from the twentieth, and no belt, bag or crumple zone has ever been designed for that.

Six bodies, worked through

Body	Mass	Speed	Kinetic energy	Equivalent drop
Tennis serve	0.058 kg	60 m/s 134 mph	104.40 J	183.55 m
Struck soccer ball	0.43 kg	30 m/s 67 mph	193.50 J	45.89 m
Cyclist	85 kg	25 km/h 16 mph	2.05 kJ	2.46 m
Rifle bullet	0.0095 kg	830 m/s 1,857 mph	3.27 kJ	35,124.12 m
Car in town	1,400 kg	50 km/h 31 mph	135.03 kJ	9.84 m
Loaded truck	40 t	80 km/h 50 mph	9.88 MJ	25.18 m

Filling in the three fields

Which quantity is missing - the energy, or the mass, or the speed. Any two of the three give you the third, and only the fields that matter to your choice stay on screen.
Mass and its unit - kilograms, grams, metric tons or pounds. Grams for a ball or a bullet, tons for anything on the road that needs a license, pounds where the source is American.
Speed and its unit - meters per second, km/h or mph, in the two modes where the speed is something you type in. The formula wants m/s, and putting km/h straight into it inflates the answer by a factor of nearly thirteen, so the selector is doing real work.
Energy and its unit - joules, kilojoules, megajoules, kilowatt hours or kilocalories, again only in the two modes that take an energy as input. A negative value is refused, because kinetic energy cannot be one.
Read the result - the headline tile holds the answer, the second tile the same energy as food and as electricity, and the third the height a fall would have to start from to match it. Two tables follow: the same body at five speeds, and where your figure sits among nine familiar ones.

Five units, and a sixth number that is not a unit

Energy is one of the few quantities where the same thing is routinely sold in five different currencies. The joule is the SI unit and it is small; everything else in the table is a convenience for a particular trade.

Unit	In joules	The car at 50 km/h	Where it is used
Joule (J)	1	135,031	Physics, everything SI
Kilojoule (kJ)	1,000	135.03	Ballistics, impact ratings, nutrition outside the US
Megajoule (MJ)	1,000,000	0.135	Vehicles, fuel content, industrial processes
Kilowatt hour (kWh)	3,600,000	0.0375	Electricity bills, battery capacity
Kilocalorie (kcal)	4,184	32.27	Food labels, where it is written Calorie

The sixth number the calculator prints is the equivalent drop, and it is not a unit at all but a translation. A body moving at v carries exactly the energy it would pick up falling from v² / 2g, so 50 km/h is a fall of 9.84 m and 100 km/h is a fall of 39.34 m. The height depends only on the speed. A truck and a tennis ball travelling side by side match the same drop, because both the energy and the mass it belongs to scale together and cancel.

Things that are true and sound wrong

A rifle bullet carries less energy than a sprinter. The bullet has 3.27 kJ, the sprinter 4.00 kJ. What separates them is not energy but the area it arrives through: the sprinter spreads it over a whole body over several seconds, the bullet delivers it through a few square millimetres in under a millisecond.

A car at 50 km/h, 31 mph, is carrying less energy than a kettle spends making one cup of tea. Its 135.03 kJ is 0.0375 kWh, and a 2,000 W kettle gets through that in 68 seconds. Motion feels expensive because it is hard to stop, not because the energy in it is large.

Slowing from 50 to 25 km/h, 31 to 16 mph, removes three quarters of the energy, not half. 135.03 kJ becomes 33.76 kJ. The square works in your favour going down exactly as hard as it works against you going up, which is why the twenty km/h you take off in a built-up area buys so much.

Kinetic energy has no direction and is never negative. Reverse the car and the velocity changes sign, but it is squared, so the energy is identical. This is exactly where energy and momentum part company: two identical cars meeting head on have zero total momentum and twice the kinetic energy of one of them.

A tennis ball would have to be dropped from 183.55 m to serve at 60 m/s, 134 mph. At 3.3 m a floor that is a fifty-five floor building, for a ball you can hold in one hand. Speeds that feel ordinary in sport are extraordinary as heights, which is the most useful reason to look at the drop column at all.

What usually needs explaining

Why is speed squared but mass is not?

Because energy is force applied over a distance, and going faster costs on both counts at once: a faster body needs a bigger force to change its motion and it covers more ground while that force acts. The two effects multiply, which is where the square comes from. Mass only affects the first, so it enters once. The practical consequence is that mass is linear and speed is quadratic, and any argument about safety or efficiency that treats them as comparable is missing the exponent.

Is the kcal here the same as a Calorie on a food label?

Yes. The capital-C Calorie used on nutrition labels is a kilocalorie, 4,184 J, which is the figure this calculator uses. So a car at 50 km/h, 31 mph, carries 32.27 kcal, which at the standard 4 kcal per gram for carbohydrate is the energy in about 8 g of sugar, two level teaspoons. The comparison is fair arithmetic and misleading intuition at the same time, which is why it is worth seeing.

Why will it not accept a negative energy?

Because there is no such thing. The velocity is squared before it reaches the mass, so the result cannot come out below zero however the body is travelling. If you have a negative figure in front of you it is a change in energy, not an energy, and it means the body lost some. Enter the amount without the sign.

Does this cover a spinning wheel or a rotating body?

No. This is translational kinetic energy, the energy of a body moving from one place to another. A spinning body also carries rotational energy, ½Iω², which needs a moment of inertia rather than a mass and is a separate calculation. For a rolling wheel the two add together, and for a solid wheel the rotation contributes roughly half as much again as the translation, so ignoring it understates a rolling body.

Why is the equivalent drop for a bullet so absurdly high?

Because the drop depends only on the speed, and 830 m/s is a speed nothing reaches by falling in air. The 35,124.12 m the calculator returns is what free fall in a vacuum would need; in real air a bullet-sized object stops accelerating at around 100 m/s and never gets close. The number is honest arithmetic about energy, not a prediction about dropping anything.

For a crash, do I use my speed or the closing speed?

It depends what you are asking. For the energy your own vehicle carries, use your own speed. For the energy that has to be absorbed when two vehicles meet, add both energies, each from its own speed and mass. What you must not do is enter the closing speed with only one car's mass: two cars at 50 km/h head on carry 270.06 kJ between them, not the 540.12 kJ that one car at 100 km/h, 62 mph, would have.

Related tools

Momentum Calculator

The quantity that survives a collision, where this one does not, and the reason a crash needs both - Open the tool

Force Calculator

Where the energy comes from and where it goes: force over a distance, in newtons, kgf or lbf - Open the tool

Braking Distance Calculator

The road length it takes to spend that energy, which grows with the same square - Open the tool

0-100 km/h Acceleration Calculator

The other end of the same problem: how long it takes to put that energy into a car in the first place - Open the tool

Speed Converter

km/h, mph and m/s in both directions, for when the speed arrives in the wrong one - Open the tool

Average Speed Calculator

Distance over time, which is usually where the speed in this formula actually comes from - Open the tool