Mass
kg
Velocity
m/s
Kinetic energy
J

# Kinetic Energy Calculator

By Mateusz Mucha and Wojciech Sas, PhD candidate

This kinetic energy calculator is a tool which helps you assess the energy of motion. It is based on the kinetic energy formula, which applies to every object in vertical or horizontal motion.

The following article will explain:

• What is kinetic energy
• How the kinetic energy formula is used
• The definition of kinetic energy
• What are some common kinetic energy units
• What is the difference between potential and kinetic energy
• How the work-energy theorem can be applied
• How the dynamic pressure and the kinetic energy equations relate to each other

## Kinetic energy definition

The encyclopedia provides the following definition of kinetic energy:

The kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains its kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.

## What is kinetic energy?

Kinetic energy is the energy of an object in motion. It provides information about how the mass of an object influences its velocity. Let's take an example. If you put the same engine into a lorry and a slick car, the former is not able to achieve the same speed as the latter because of its mass. You can easily find it out by using our kinetic energy calculator.

## Kinetic energy formula

The kinetic energy formula defines the relationship between the mass of an object and its velocity. The kinetic energy equation is as follows:

`KE = 0.5 * m * v²`,

where:

• `m` - mass,
• `v` - velocity.

With the kinetic energy formula, you can estimate how much energy is needed to move an object. The same energy could be used to decelerate the object, but keep in mind that velocity is squared. This means that even a small increase in speed changes the kinetic energy by a relatively high amount.

How about you give our kinetic energy calculator a try? This tool do any and every calculation for you after typing the mass and velocity of an object. It even works in reverse, just input any two known variables and you will receive the third! If you don't know the speed of the object, you can easily calculate it with our velocity calculator.

You should be aware, however, that this formula doesn't take into account relativistic effects, which become noticeable at higher speeds. If an object is moving faster than 1% of the speed of light (approximately 3,000 km/s, or 3,000,000 m/s), you should use our relativistic kinetic energy calculator.

## Kinetic energy units

The units of kinetic energy are precisely the same as for any other type of energy. The most popular and commonly used kinetic energy units are:

• Joule (J), equivalent to kg * m² / s² - SI unit,
• Foot-pound (ft·lb) - imperial unit,
• Electronvolt (eV),
• Calorie (cal),
• Watt-hour (Wh).

All of these kinetic energy units can be easily converted into one another with the following ratios: `1 J = 0.7376 ft·lb = 6.242·10¹⁸ eV = 0.239 cal = 2.778·10⁻⁴ Wh.`

As you can see, depending on the scale, they may differ by a significant number of orders of magnitude, so it's convenient to use scientific notation or express them with some prefix like kilo- (kcal, kWh), Mega- (MeV), etc. Anyway, you don't need to worry about the units while using our kinetic energy calculator; you can choose whichever you like by clicking on the units, and the value will be immediately converted.

## Potential and kinetic energy

Potential energy refers to the gravitational pull exerted on an object, relative to how far it has to fall. When the object gains altitude, its potential energy increases. If you want to check what potential energy is and how to calculate it, use our potential energy calculator.

## The work-energy theorem

It turns out that kinetic energy and the amount of work done in the system are strictly correlated, and their relation can be described by the work-energy theorem. It states that the work done by all external forces is converted into a change of kinetic energy:

`W = ΔKE = KE₂ – KE₁`.

Actually, there are several types of kinetic energies. We can distinguish:

1. Translational kinetic energy - the most well-known type. It's related to the motion of an object traveling in a particular direction and the distance it covers in a given time. This is the kind of energy which you can estimate with this kinetic energy calculator.

2. Rotational kinetic energy - as the name suggests, it takes into account the motion of a body around an axis.

3. Vibrational kinetic energy - can be visualized as when a particle moves back and forth around some equilibrium point, approximated by harmonic motion. Depending on the structure it can be shown as stretching, twisting, or bending.

At the microscopic scale, all of these kinetic energy examples are manifestations of thermal energy, which increases as the temperature rises.

## The relation between dynamic pressure and kinetic energy

The expression of the dynamic pressure (caused by fluid flowing) is the following:

`p = ρ * v² / 2`.

It looks very similar to the kinetic energy equation because mass is replaced by the density, and it isn't a coincidence. The other name for dynamic pressure is kinetic energy per unit volume, and analogically, density is defined as the mass contained in a particular volume. With just a pinch of imagination, you can use our kinetic energy calculator to estimate the dynamic pressure of a given fluid. If you replace mass in kg with density in kg/m³, then you can think about the result in J as the dynamic pressure in Pa.

## Kinetic energy examples

You're sitting in class and your teacher tells you that the kinetic energy of an object equals 1 J. What do you think - is that a lot, or not really? The key information is what kind of object we are talking about. Let's take a look at some computational kinetic energy examples to get to grips with the various orders of magnitude:

1. Some of the highest energy particles produced by physicists (e.g., protons in Large Hadron Collider, LHC) reach the kinetic energy of few TeV. It is said to be comparable with the kinetic energy of a mosquito. It's impressive when you realize what an enormous number of molecules is there in one insect. However, if we work out the value in joules, then the outcome is in the order of `1 μJ`. Based on that, an individual particle with the kinetic energy of `1 J` is extraordinarily high-energy and surely not going to be produced by humanity any time soon.

2. Let's consider a bullet of mass `5 g`, traveling at a speed of `1 km/s`. Its kinetic energy equals `2,500 J`, way above `1 J` because of the considerable velocity. That's the reason why bullets cause a lot of damage while reaching targets. Use the kinetic energy calculator to find out how fast that the same bullet will have to be traveling at to get its energy to `1 J`. It's a velocity of about `20 m/s`. Well, it will still hurt when it impacts a body, but it definitely won't cause anything worse than a bruise.

3. The ship weighs `50,000 tons` and can move at the speed of `10 knots`. We can always use speed converter to find that it's around `5.1 m/s`. Its kinetic energy is then roughly `661 MJ`. That number is obtained mainly because of its impressive mass.

Mateusz Mucha and Wojciech Sas, PhD candidate

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