Kinetic Energy Calculator

1. Enter any two of kinetic energy, mass and speed.
2. Leave the one you want to find blank.
3. Read the result.
4. See which value was solved for and the formula used.

Here is what each result means:

Kinetic energy is the energy an object has because it is moving. It depends on the mass and the speed, by the formula KE equals one half times mass times speed squared. Because the speed is squared, going twice as fast gives four times the kinetic energy, not twice.

In SI units, kinetic energy is measured in joules. It is the energy that must be supplied to speed an object up, and the energy released when it slows down. Kinetic energy is central to mechanics, from braking distances to collisions, and this calculator links it to mass and speed so you can find any one from the other two.

The squared speed is why road safety campaigns focus so heavily on speed. A car at 60 carries not just a bit more energy than one at 30, but four times as much, all of which must be absorbed in a crash. That single squared term turns a modest speed increase into a large jump in the energy involved.

It rearranges one formula to solve for whichever value you leave blank.

1. For energy, multiply half the mass by the speed squared.
2. For mass, use twice the energy over the speed squared.
3. For speed, take the square root of twice the energy over the mass.

The mass here is the same one used in the force calculator, linking motion, force and energy.

A 2 kilogram object moves at 3 meters per second.

Calculation: KE = (1/2)(2)(3)^2 = (1/2)(2)(9) = 9 joules. If the speed doubled to 6, the energy would be four times as much, 36 joules, because speed is squared.

Kinetic energy rises with the square of speed but only in proportion to mass.

This is why a small rise in speed makes a large difference to braking distance and to the severity of a crash.

The two main forms of mechanical energy describe different states.

A falling object trades potential energy for kinetic energy as it speeds up, with the total staying the same when friction is ignored.

The Speed

The biggest factor, since it is squared. A small increase in speed raises the energy sharply.

The Mass

Energy scales directly with mass, so a heavier object at the same speed carries more energy.

The Reference Frame

Speed, and so kinetic energy, is measured relative to something. A different reference frame gives a different value.

Physics Homework

Find the energy of a moving object, or work back to its mass or speed.

Safety and Motion

Reason about braking, impacts and how speed multiplies energy.

Engineering

Estimate the energy a moving part or vehicle carries.

1. Forgetting to Square the Speed

The speed is squared before halving. Missing that greatly understates the energy.

2. Leaving Out the One Half

Kinetic energy is one half m v squared, not m v squared.

3. Using Weight for Mass

Use mass in kilograms, not weight in newtons.

4. Mixed Units

Use consistent units, ideally joules, kilograms and meters per second.

5. Ignoring the Reference Frame

Speed is relative. State what the motion is measured against.

The formula is exact; only the displayed decimals are rounded.

It is the energy an object has because it is moving. It equals one half times the mass times the speed squared. A faster or heavier object has more kinetic energy.

Multiply one half by the mass and by the speed squared. A 2 kilogram object at 3 meters per second has an energy of one half times 2 times 9, which is 9 joules.

Because energy grows with the square of speed. Doubling the speed gives four times the energy, not twice, which is why speed matters so much for impacts and braking.

Take the square root of twice the energy divided by the mass. Leave the speed field blank and enter energy and mass, and the calculator solves for it.

Use twice the energy divided by the speed squared. Leave the mass field blank and enter energy and speed to solve for the mass.

The SI unit is the joule, when mass is in kilograms and speed in meters per second. Keep your units consistent for a correct result.

Kinetic energy comes from motion and depends on mass and speed. Potential energy comes from position, such as height. A falling object trades one for the other.

No. It depends only on the mass and the speed, not the direction of travel. Two objects moving the same speed in different directions have the same kinetic energy.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Kinetic energy (Wikipedia).
• Kinetic energy explained (Maths Is Fun).
• Joule (Wikipedia).