Kinetic Energy Calculator

How to use this tool

Pick what you want to find. The default finds the kinetic energy from a mass and a speed, and the other two modes turn the formula round to give the speed from an energy and a mass, or the mass from an energy and a speed. Type the two known values, choose their units from the menus beside them, and the third box fills in with the answer in the highlighted colour. The energy unit can be left on "J, kJ or MJ" and the tool picks the sensible one, or set to foot pounds force, kilowatt hours or calories if that is what you need. The stopping distance box only feeds the force figure: it is the distance over which the object comes to rest, such as the crumple depth of a car or the penetration of a bullet.

The input people most often get wrong is the speed unit. A speed typed as 100 with m/s selected is 360 km/h, and the energy comes out 13 times too high, because the 3.6 conversion is squared. Check the unit menu before reading the answer, and check the mass unit too: lb and kg differ by a factor of 2.2, and grains are a different unit from grams altogether. The note under the inputs always repeats the mass in kilograms and the speed in metres per second, so a slip shows up at once.

What the calculation is doing

Kinetic energy is the work it took to bring a mass up to speed, and equally the work needed to bring it back to rest: KE = ½mv². With the mass in kilograms and the speed in metres per second the result is in joules. Everything else in the tool is unit conversion around that one line. Pounds become kilograms at exactly 0.45359237, grains at 64.79891 mg each, miles per hour become metres per second at exactly 0.44704, km/h by dividing by 3.6, feet per second at 0.3048 and knots at 1,852 m per hour. Joules go out again as kilojoules, megajoules, foot pounds force at 1.3558179 J each, kilowatt hours at 3.6 million joules, or thermochemical calories at 4.184 J, all from NIST Special Publication 811.

The other two modes are the same equation rearranged: speed = √(2 × energy ÷ mass) and mass = 2 × energy ÷ speed². Alongside the main answer the tool gives momentum, p = mv, because the two are constantly confused and behave differently. The drop height, h = v² ÷ 2g with g = 9.80665 m/s², is the fall in a vacuum that would reach the same speed. The average stopping force is the energy divided by the stopping distance, which follows from the work energy theorem when the force is taken as constant, and the matching deceleration is v² ÷ 2d. Dividing that by g gives the figure in g, and it equals the drop height divided by the stopping distance, a handy check.

Why the square matters more than the number

Most quantities people deal with day to day scale in a straight line: twice the fuel, twice the range. Kinetic energy does not, and the consequences are physical, not academic. The 1,500 kg car in the diagram carries 52.08 kJ at 30 km/h and 833.3 kJ at 120 km/h. The speed went up four times and the energy sixteen. Brakes turn that energy into heat, and a barrier or another vehicle absorbs it by deforming, so the damage available in a crash tracks the square of the speed, not the speed itself. Reading the speedometer as a measure of risk understates the top end badly.

The drop height makes the same point without any units to argue about. A fall from 9.8 m, about a third floor window, reaches 50 km/h. Reaching 100 km/h takes a fall from 39.3 m, a thirteen storey building, and 120 km/h needs 56.7 m. Nobody would step off the thirteenth floor expecting a good outcome, yet 100 km/h feels ordinary from the driving seat. The height depends only on the speed, so the same picture applies to a cyclist, a motorbike or a train.

Momentum is the other line on the chart, and it is worth keeping the two apart. Momentum is mass times speed and it grows in a straight line, which is why the dashed line in the tool is straight while the energy curve bends upward. Collisions conserve momentum, so it decides how the wreckage moves afterwards. Energy decides how much crushing, heating and breaking happens on the way. An 8 g rifle bullet at 900 m/s has a momentum of 7.2 kg·m/s, less than a walking person, but it carries 3.24 kJ, delivered over a few centimetres of penetration, and the force figure in the tool shows what that does: 3,240 J over 10 cm is an average of 32.4 kN.

Kinetic energy of vehicles at road speeds

The energy in kilojoules for a small car, a family car and a large SUV, and in megajoules for a loaded 40 tonne truck, with the speed in the three common units and the drop height that reaches it. The drop height does not depend on the mass.

A worked example you can check on paper

The tool opens with a 1,500 kg car at 100 km/h and a stopping distance of 1 m. Speed in m/s = 100 ÷ 3.6 = 27.7778 m/s. Kinetic energy = ½ × 1,500 × 27.7778² = ½ × 1,500 × 771.605 = 578,704 J, shown as 578.7 kJ. In foot pounds force that is 578,704 ÷ 1.3558179 = 426,830 ft lbf, and in kilowatt hours 578,704 ÷ 3,600,000 = 0.1608 kWh, about ten minutes of a 1 kW heater.

Momentum = 1,500 × 27.7778 = 41,667 kg·m/s. Drop height = 27.7778² ÷ (2 × 9.80665) = 39.34 m. Stopping over 1 m, the average force = 578,704 J ÷ 1 m = 578.7 kN, the deceleration = 27.7778² ÷ (2 × 1) = 385.8 m/s², which is 39.3 g, and it is all over in 2 × 1 ÷ 27.7778 = 0.072 s. Turning it round, ask what speed 500 kJ gives the same car: √(2 × 500,000 ÷ 1,500) = √666.667 = 25.82 m/s = 92.95 km/h, which the speed mode reproduces.

Mistakes that catch people out

Squaring the wrong unit. Putting km/h or mph straight into ½mv² gives a number, but not joules. The error is the conversion factor squared: 12.96 for km/h and about 5 for mph. Convert the speed to m/s first, or let the unit menu do it.

Mixing up pounds and slugs. In US customary units the pound is a weight, and the formula needs mass in slugs (weight ÷ 32.174 ft/s²) to give foot pounds force from feet per second. The tool avoids the trap by converting everything to kilograms and metres, but a hand calculation with pounds and ft/s directly comes out 32 times too high.

Calories that are really kilocalories. A food Calorie is 4,184 J, a thousand small calories. The cal option here is the small thermochemical calorie of 4.184 J; pick kcal for food energy. The 578.7 kJ of the default car is 138.3 kcal, a little more than the food energy in a banana.

Reading the stopping force as a peak. Energy ÷ distance is the average force over the whole stopping distance. Real impacts ramp up and peak at two or three times the mean, so use the figure as a floor when sizing an anchor, a barrier or a lanyard, not a ceiling.

Forgetting the energy that is spinning. Wheels, flywheels and rotors carry rotational kinetic energy on top of the ½mv² of their centre of mass. For a car it is a few percent extra; for a grinding wheel or a helicopter rotor it is the whole story, which is what the spinning object panel is for.

Popular calculations

Each address opens the calculator with those figures filled in, and everything can be changed once it is open.

Cars, trucks and boats

People, sport and everyday objects

Bullets and ballistics

Speed from energy and mass

Mass from energy and speed

How this was checked

Every conversion factor in the engine was compared with the value printed in NIST Special Publication 811, Appendix B.9. The pound is 0.453 592 37 kg, the grain 6.479 891 × 10^−5 kg, the mile per hour 0.447 04 m/s and the foot 0.3048 m. The knot is 1,852 m per hour, the kilowatt hour 3.6 × 10^6 J, the thermochemical calorie 4.184 J and the foot pound force 1.355 818 J. The exact factors agree to every digit and the derived ones agree with the seven figure printed values to better than one part in ten million. The International Table calorie of 4.1868 J was deliberately not used; it would move the calorie figures by 0.07%.

The formula was then tested against published worked examples. OpenStax University Physics Example 7.6 gives 4.0 kJ for an 80 kg athlete at 10 m/s, 1.7 × 10^15 kg for an asteroid releasing 4.2 × 10^23 J at 22 km/s, and 4.1 × 10^−21 J for a neutron of 1.68 × 10^−27 kg at 2.2 km/s. The engine returns 4,000 J, 1.736 × 10^15 kg and 4.066 × 10^−21 J, each rounding to the printed answer. Example 7.10 in the same book finds an average stopping force of 960 N for a 2.60 g bullet at 335 m/s that penetrates 15.2 cm, and the engine gives 959.8 N. College Physics 2e Examples 7.2 and 7.4 give 3.75 J for a 30 kg package at 0.5 m/s and 2.53 m/s for the same package with 95.75 J; the engine matches both. The momentum figure of 21,000 kg·m/s for a 1,400 kg car at 15 m/s and the helicopter rotor energy of 5.26 × 10^5 J in Example 10.9 were reproduced as well.

Independent routes were run in a Node script kept with the build. Round trips from energy to speed and back, energy to mass and back, and drop height to speed and back agreed to within 3 parts in 10^16 over 5,000 random cases. Foot pound results were recomputed through the slug based US customary route on 3,000 random bullet loads and agreed to 1 part in 10^14, and the shooting table shortcut of grains × fps² ÷ 450,240 was confirmed to read 0.044% high. The stopping force identities F × d = E and a ÷ g = h ÷ d held to 1 part in 10^12. Every address in the lists above was then loaded and checked for a distinct title, a matching canonical address and a clean answer, and the tool itself was checked for layout, chart rendering and CSV, image and print output at desktop, tablet and phone widths.

Common questions

What is the formula for kinetic energy?

Kinetic energy = ½ × mass × speed², written KE = ½mv². With the mass in kilograms and the speed in metres per second the answer is in joules. A 1,500 kg car at 27.78 m/s (100 km/h) has ½ × 1,500 × 27.78² = 578,704 J, or 578.7 kJ. The calculator converts pounds, grains, km/h, mph, feet per second and knots into those base units before applying the formula, then converts the joules into whatever energy unit you pick.

Why does doubling the speed quadruple the kinetic energy?

Because the speed is squared. Kinetic energy is the work needed to accelerate the mass, and the distance covered while accelerating grows with the square of the final speed at a fixed force. Going from 50 to 100 km/h takes the 1,500 kg car from 144.7 kJ to 578.7 kJ, four times as much, while the momentum only doubles from 20,833 to 41,667 kg·m/s. The same square law is why stopping distance grows so quickly with speed.

What is the difference between kinetic energy and momentum?

Momentum is mass × speed, measured in kg·m/s, and it is what a collision conserves. Kinetic energy is ½ × mass × speed², in joules, and it is what has to be absorbed to bring something to rest. Two objects can have the same momentum and very different energies: a 40 tonne truck rolling at 1 km/h and a 1,500 kg car at 26.67 km/h both have a momentum of 11,111 kg·m/s, but the truck carries 1.543 kJ and the car 41.15 kJ, 27 times as much. The chart in the calculator shows momentum as a straight line and energy as a curve for that reason.

How do I work out bullet energy in foot pounds?

Enter the bullet weight in grains, the muzzle velocity in feet per second, and pick ft lbf as the energy unit. A 150 grain bullet at 2,800 ft/s carries 2,611 ft lbf, which is 3,540 J. The shortcut used in shooting tables, grains × velocity² ÷ 450,240, gives 2,612 ft lbf for the same load; the exact constant from the NIST factors is 450,437, so the shortcut reads about 0.04% high. One foot pound force is 1.3558 J.

What does the drop height mean?

It is the height an object would have to fall, with no air resistance, to reach the same speed: h = v² ÷ 2g with g = 9.80665 m/s². At 100 km/h the drop height is 39.34 m, so hitting a wall at that speed is like driving off a 13 storey building. The figure does not depend on the mass, only on the speed, and it is a useful way to picture how much harder a speed is than the one below it.

Does the calculator handle spinning objects and very high speeds?

The panel below the table gives rotational kinetic energy ½Iω² for a disc, a sphere, a hoop, a shell and a rod, using the standard moments of inertia. The default 10 kg disc of 30 cm radius at 300 rpm carries 222.1 J. For speeds above about a tenth of the speed of light the classical formula reads low, by 0.76% at that speed and more beyond it; the tool adds a note with the correction when a speed that high is entered.

Related Calculators and Reference

• Speed, Distance and Time Calculator: get the speed from a distance and a time before bringing it here.
• Speed Converter: km/h, mph, knots, m/s, ft/s and Mach when you only need the speed itself converted.
• Energy Converter: joules, kWh, BTU and calories for energies that did not start as motion.
• Kg to Lbs Converter: the mass conversion on its own, with the reverse direction.
• Force Unit Converter: turn the stopping force in newtons into lbf, kgf or kip.
• Projectile Motion Calculator: range, flight time and peak height from launch speed and angle, with optional air drag.
• Stopping Distance Calculator: reaction plus braking distance for a given speed and road surface.
• NIST SP 811 Appendix B.9: the conversion factor table every unit in this tool is taken from.