Kinetic Energy Calculator

This kinetic energy calculator will calculate the energy of a moving object based on its mass and velocity using the formula KE = (1/2) * m * v^2. Enter mass and velocity to find kinetic energy, or leave one of the three fields blank to solve for that value. The result can be shown in joules, foot-pounds, calories, kilowatt-hours, electron volts, or tons of TNT.

What is Kinetic Energy?

Kinetic energy is the energy an object has because of its motion. Any object with mass that is moving has kinetic energy. Examples include a person walking, a rolling ball, flowing water in a river, a bullet fired from a gun, or a planet orbiting the sun. The faster an object moves and the greater its mass, the more kinetic energy it has.

This is the work required to accelerate an object from rest to its current velocity. Once in motion, an object retains this energy until something slows it down. When the object comes to a stop again, it can exert just as much work on whatever it collides with. Kinetic energy is a scalar quantity, meaning that it has only magnitude and no direction. Since mass is positive and the square of velocity is also positive, kinetic energy can never be negative.

The formula for kinetic energy is:

The kinetic energy of an object is equal to half its mass multiplied by the square of its speed.

In this formula KE stands for kinetic energy, m is mass and v is velocity. If the mass is in kilograms and the velocity is in meters per second then the unit of the calculated energy will be joules. A joule is equal to a kilogram times meter squared divided by a second squared. The calculator converts units so you can also enter grams or miles per hour and get meaningful results.

How to use this calculator:

Enter two known values and leave the unknown field blank. To calculate kinetic energy, enter mass and velocity and leave the energy field blank. To find the required speed of an object given its energy, enter mass and kinetic energy and leave the velocity field blank. To calculate mass, enter velocity and kinetic energy.

You do not have to select a mode. Leaving the field blank will instruct the calculator to determine the value of that field, allowing you to perform all three types of calculations with the same interface.

Calculating speed or mass:

As KE = m v² / 2 is an equation that contains three quantities it can be rearranged to calculate any one of these quantities. The calculator uses the following formula in the background:

Why does speed double while energy quadruples?

The effect of speed is much greater than the effect of mass. Because the speed is squared, kinetic energy quadruples when the speed doubles and triples when the speed triples. Mass only has a single calculation, so doubling the mass will only double the energy.

This is one of the most important facts about kinetic energy and a law that has significant real world implications. A car going 60 mph has four times as much energy as one going 30 mph. So braking distances and damage from collisions increase dramatically when speed increases. The calculator's kinetic energy vs velocity graph shows this steep rise, and the "doubling of speed" map clearly explains the factor of Four.

A practical example of calculation:

What is the kinetic energy of an object with a mass of 10kg and a velocity of 5m/s? Enter the mass as 10 kilograms and the velocity as 5 meters per second.

So the energy that this object has is 125 joules. If it accelerates to 10 m/s, then its energy goes up to 500 joules. Even though the speed only doubled, it's four times as high as originally.

The kinetic energy of everyday objects

When actual values are put into the equation, it becomes apparent how wide a range of kinetic energy there is and what effect speed and mass have on the result.

A bullet has a small mass but because of its very high speed it has a large amount of energy. This is why it can cause serious damage. A ship on the other hand has a low speed but because of its huge mass it has an amazing amount of energy. That's why it takes many miles to stop.

The work and energy theorem

Kinetic energy and work are like two sides of the same coin. According to the work-energy theorem, the total work done on an object equals the change in its kinetic energy.

When you push an object its kinetic energy increases and when you apply braking or friction forces in the opposite direction, kinetic energy is removed. This is why brakes get hot. The brakes convert a car's kinetic energy into heat energy. You can use a calculator to open up the work equation and enter an initial velocity to find out how much work was done.

Kinetic energy and potential energy

Energy changes between different forms but is not destroyed. When an object falls the potential energy caused by gravity is converted into kinetic energy, increasing speed. As an object rises the direction of the energy change is reversed and the speed decreases. A roller coaster uses this exchange to convert height into speed as it descends and then converts that speed back into height as it ascends.

If kinetic energy is set equal to potential energy (mgh), then the height required to achieve a particular velocity is found by dividing the square of the velocity by 2g. The mass does not matter. The fall calculator tools calculate this value based on the velocity.

Translational kinetic energy and rotational kinetic energy

This calculator deals with the translational kinetic energy an object has when it moves from one position to another. Objects that rotate, such as a rolling wheel, have rotational kinetic energy in addition to their translational motion, and its magnitude is determined by the moment of inertia and the angular velocity. The total kinetic energy of a rolling object is the sum of the translational and rotational parts. For calculations in case of pure rotation, a separate calculator for rotational kinetic energy should be used.

Relativistic kinetic energy.

The formula KE = mv²/2, where v is squared and divided by two, is a very accurate approximation for everyday speeds but it no longer holds true when an object approaches the speed of light. When the velocity exceeds 1% of the speed of light, or about 3,000 kilometers per second, the actual kinetic energy begins to exceed values calculated using Newtonian mechanics' formula.

As the speed approaches that of light, the Lorentz factor gamma becomes infinite and so does the kinetic energy. Therefore an object with mass can never quite reach the speed of light. If you open the Relativity box, you can see the Lorentz factor, actual kinetic energy, and how much Newtonian mechanics underestimates the values. You can also change the units for velocity to enter it as a ratio to the speed of light.

Kinetic energy units:

The units for kinetic energy are the same as those for other forms of energy. The SI unit is the joule, but since it is often more intuitive to express results in other units, the calculator offers several options. Foot-pounds are commonly used in ballistics, kilowatt-hours for power, calories in nutrition and electron volts in particle physics, while tons of TNT are used as a unit for very large amounts of energy.

One joule is approximately equal to 0.7376 foot-pounds, 0.239 calories, or 2.778 × 10^-4 watt-hours and about 6.242 × 10^18 electron volts. The calculator automatically converts between these units so you can compare the kinetic energy of a bullet in foot-pounds to the kinetic energy of a meal in calories, for example.

Applications of kinetic energy:

Kinetic energy plays an important role in many areas of everyday life and technology. The energy generated by wind turbines from the flowing air stream as well as the energy produced by hydroelectric dams from falling water streams are both examples of kinetic energy. How deep a hammer drives a nail, how far a car needs to travel before coming to a stop, and what damage is caused by a bullet or hailstone hitting a target all depend on kinetic energy.

Kinetic energy can also be explained in sports. A faster throw, a heavier club and a more powerful swing all give the ball more kinetic energy. The concepts of kinetic energy are also applicable on cosmic scales. Meteorites have very high kinetic energy when they enter Earth's atmosphere, which is why most of them turn into light and heat as they burn up while rushing through the atmosphere.

Common mistakes:

Some mistakes can easily lead to errors. First of all there is the risk of forgetting the factor squaring the speed. As energy is proportional to the square of the speed (v²), a small deviation in the speed leads to a large deviation in the calculated energy. Secondly, there might be confusion about units. To get a direct result in Joules, mass and speed must be given in kilograms respectively meters per second. However this calculator automatically converts all entered units so that this mistake is avoided.

Thirdly, there is a misconception that kinetic energy can be negative or have direction. Neither of these are possible. Since the velocity is squared, an object moving to the left has the same kinetic energy as the same object moving to the right at the same speed.