Kinetic Energy Calculator

kinetic energy = ½ × mass × velocity² equivalent fall height = velocity² ÷ ( 2 × g )

m

Mass in kilograms — the field also takes pounds, tonnes and grams, and converts them before the formula runs

v

Velocity in metres per second — the field also takes km/h, mph, ft/s and knots. It is the speed, not the velocity vector: this page measures how much energy there is, not which way it points

g

Standard gravity, 9.80665 m/s² — the fixed value the fall height is measured against, not the local value at your latitude

h

Equivalent fall height in metres — the drop that would leave an object at that speed, from v² ÷ 2g, the same relation the reference table uses

Reach for this page whenever something moves and you care how much damage it can do or how much energy you have to put in or take out. The usual jobs are comparing two speeds on the same vehicle, sizing a brake or a barrier, and sanity-checking a claim about a crash test. Two habits make the answers more useful. First, keep the speed in the unit you actually drive in — the field converts for you, so there is no reason to hand-convert to m/s and lose a digit. Second, read the fall height rather than the joules: 538 kJ means little to most people, while 'the same energy as falling from the twelfth floor' is a sentence anyone can act on. If instead you are asked what a body weighs under gravity, that is a different page — this one never calls it weight.

1. A 3,300 lb car at 60 mph

   1. 3,300 lb = 1,496.855 kg (the field takes kilograms, so the pounds go in the mass unit dropdown)
   2. 60 mph = 26.8224 m/s
   3. Velocity squared: 26.8224 × 26.8224 = 719.441
   4. Kinetic energy: ½ × 1,496.855 × 719.441 = 538,449 J
   5. The same number in the other two units: 538.449 kJ, and 538,449 ÷ 1.3558179 = 397,140 ft·lb
   6. Equivalent fall height: 719.441 ÷ ( 2 × 9.80665 ) = 36.7 m, or 120 ft

   This is the reference table's row, read the other way round: the table starts from the speed and gives the energy, and this example starts from the same car. Compare it with the 55 mph row — 55 mph is 333,708 ft·lb against 397,140 at 60, and the ratio of the energies (1.19) is the ratio of the speeds squared (1.19), not the ratio of the speeds (1.09). The 36.7 m fall height is the part worth saying out loud: it is a building, not a kerb.

2. A rifle bullet, 0.008 kg at 800 m/s

   1. Mass: 0.008 kg, which is the 8 g the box says
   2. Velocity squared: 800 × 800 = 640,000
   3. Kinetic energy: ½ × 0.008 × 640,000 = 2,560 J
   4. In the other two units: 2.56 kJ, and 1,888 ft·lb
   5. Equivalent fall height: 640,000 ÷ ( 2 × 9.80665 ) = 32,631 m

   This one is here to break the intuition that fast and light means little energy: 8 g is a quarter of an ounce, and it still carries more energy than a bowling ball dropped from a first-floor window. It is also the example that shows the square at work — the same bullet at 400 m/s carries 640 J, a quarter as much, not half. The 32.6 km fall height is not a thing anyone does; it is the number that says the speed, not the mass, is doing the work here.

3. A 70 kg runner at 3 m/s

   1. Velocity squared: 3 × 3 = 9
   2. Kinetic energy: ½ × 70 × 9 = 315 J
   3. In the other two units: 0.315 kJ, and 232 ft·lb
   4. Equivalent fall height: 9 ÷ ( 2 × 9.80665 ) = 0.46 m

   The everyday end of the scale, and the one that makes the bullet example land: a jogging adult carries about 315 J, and stopping takes that much work no matter how gently you do it. It is also why the fall height is more honest than the joules — 0.46 m is a step off a kerb, and 315 J sounds like a lot until you see where it comes from. Run the same person at 6 m/s and it is 1,260 J: twice the speed, four times the energy, which is the whole point of the page.

This page does not do rotational kinetic energy. A spinning flywheel, a rolling wheel and a turning shaft carry ½Iω² on top of the ½mv² of their centre of mass, and the page adds neither the rotational part nor the moment of inertia that goes with it. It is also a low-speed formula: below roughly a tenth of the speed of light it is within about one percent, and above that it understates the energy, because the relativistic expression grows faster than v². It treats the object as a point — no deformation, no energy going into crumpling the metal, which is exactly the energy a crash test is interested in and exactly what this page cannot give you. It does not know where the energy came from or where it goes: an engine putting it in, brakes turning it into heat, or a fall trading height for speed are all outside the chain. Finally, it says nothing about the direction of motion, because energy has none — if you need the vector, momentum is the quantity you are after.

What is the kinetic energy of a 3,300 lb car at 60 mph?

538,449 J, which is 538.449 kJ or 397,140 ft·lb. The working is ½ × 1,496.855 kg × (26.8224 m/s)², and the equivalent fall height is 120 ft — the same energy the car would carry after dropping from a twelve-storey building. That last reading is the one to quote: the joules are correct and nobody can picture them.

How do I calculate kinetic energy?

Square the velocity, multiply by the mass, and halve it. For a 70 kg runner at 3 m/s that is 9 × 70 ÷ 2 = 315 J. The field takes the speed in whatever unit you drive or run in — km/h, mph, m/s, ft/s or knots — and converts to metres per second before the formula runs, so there is no need to convert by hand and lose a digit on the way.

Why does the energy depend on the square of the speed?

Because the work done on an object is force times the distance it travels while that force acts, and at a higher speed the object covers more distance in the same time. Push a body from rest to v and the average speed is v/2 while the momentum gained is mv, so the work comes out as ½mv². That is also why the stopping distance of a car grows with the square of the speed while the braking force stays roughly the same — the brakes have to shed four times the energy from twice the speed.

Does mass matter as much as speed?

No, and the difference is the point of the formula. Energy is proportional to mass but to the square of velocity, so doubling the mass doubles the energy while doubling the speed quadruples it. An 8 g rifle bullet at 800 m/s carries 2,560 J; the same bullet at 400 m/s carries 640 J, and a 70 kg runner at 3 m/s carries 315 J. Light and fast beats heavy and slow once the speed ratio is large enough.

How do I convert kinetic energy to foot-pounds?

Divide the joules by 1.3558179483314004, or read the ft·lb row the page already prints. 538,449 J is 397,140 ft·lb. The factor is exact by definition — one foot is 0.3048 m and one pound is 0.45359237 kg — so the conversion adds no error of its own; the numbers only disagree in the last digit because both rows are rounded for display.

What is the equivalent fall height?

The height an object would have to fall through, with no air resistance, to reach that speed: v² ÷ 2g. It is the same energy expressed as a height, which is why it is easier to picture than joules. A car at 60 mph carries the energy of a 120 ft fall, and a bullet at 800 m/s the energy of a 32.6 km one. Real falls lose a little to air resistance, so the real drop needed is slightly larger — the height is a lower bound, and close enough below about 30 m/s.

• Kinetic Energy and the Work-Energy Theorem (College Physics 2e, §7.2) — the derivation of ½mv² from the work done accelerating a body from rest — OpenStax
• NIST Guide to the SI — the joule as the derived unit kg·m²/s², and the exact conversion factors this page uses for foot-pounds (1.3558179483314004 J) and for mph and lb — National Institute of Standards and Technology
• Kinetic energy — the classical and relativistic expressions, and where the low-speed form stops being good enough — Wikipedia