# How to calculate kinetic energy

### Definition

Kinetic energy is the energy possessed by a body, object or particle due to its motion. In other words, any object, body or particle with a mass and speed has kinetic energy. An object, body or particle with zero speed (which means that it’s stationary) will have zero kinetic energy.

Image: Kinetic energy of a bullet

Even if it has low mass, a bullet fired from a gun has a relatively high kinetic energy due to the fact that it’s travelling at very high speed.

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### Formula

To calculate kinetic energy multiply the mass of the body (object) with the square value of the speed and divide the result to two. The formula (equation) to calculate kinetic energy is [1]:

Ek = (m · v2) / 2
(1)

where:

• Ek [J] – kinetic energy
• m [kg] – mass
• v [m/s] – speed

The unit of measurement of kinetic energy is joule [J].

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### Vehicle example

Calculate the kinetic energy of a vehicle of mass 1200 kg, travelling at a speed of 125 kph.

Step 1. Convert the vehicle speed from [kph] to [m/s], by dividing the [kph] value to 3.6:

v = 125 / 3.6 = 34.72 m/s

Step 2. Calculate the kinetic energy Ek [J] of the vehicle using equation (1):

Ek = (m · v2) / 2 = (1200 · 34.722) / 2 = 723287.04 J

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### Bullet example

Calculate the kinetic energy of a bullet of mass 30 g, travelling at a speed of 2600 feet per second.

Step 1. Convert the bullet’s mass from [g] to [kg], by dividing the [g] to 1000:

m = 30 / 1000 = 0.03 kg

Step 2. Convert the bullet’s speed from [ft/s] to [m/s], by dividing the [ft/s] value with 3.281:

v = 2600 / 3.281 = 792.44 m/s

Step 3. Calculate the kinetic energy Ek [J] of the bullet using equation (1):

Ek = (m · v2) / 2 = (0.03 · 792.442) / 2 = 9419.42 J

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### Calculator

The kinetic energy calculator allows you to calculate the kinetic energy of a body (object) with a given mass and travelling speed. You need to enter the mass and speed parameters and choose the desired unit of measurement.

The default unit of measurement for energy is Joule. If you want the result displayed in another unit, use the dropt down list to choose and click the CALCULATE button again.

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### Kinetic energies for various objects

Object Mass [kg] Speed [m/s] Kinetic energy [J]
Earth orbiting the Sun 5.98·1024 2.98·104 2.65·1033
Moon orbiting the Earth 7.35·1022 1.02·103 3.82·1023
Rocket moving at escape speeda 500 1.12·104 3.14·1010
Automobile at 55 miles per hour 2000 25 6.3·105
Running athlete 70 10 3500
Stone dropped from 10 m 1 14 98
Golf ball at terminal speed 0.046 44 45
Raindrop at terminal speed 3.5·10-5 9 1.4·10-3
Oxygen molecule in air 5.3·10-26 500 6.6·10-21

a escape speed is the minimum speed an object must attain near the Earth’s surface if it is to escape the Earth’s gravitational force.

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### References

[1] David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 7th edition, John Wiley & Sons, 2004.
[2] Benjamin Crowell, Light and Matter – Physics, 2007.
[3] Raymond A. Serway and John W. Jr. Jewett, Physics for Scientists and Engineers, 6th edition, Brooks/Cole Publishing Co.,2004
[4] Jiansong Li, Jiyun Zhao, and Xiaochun Zhang, A Novel Energy Recovery System Integrating Flywheel and Flow Regeneration for a Hydraulic Excavator Boom System, Energies 2020.
[5] Leo H. Holthuijsen, Waves in oceanic and coastal waters, Cambridge University Press, 2007.
[6] Kira Grogg, Harvesting the Wind: The Physics of Wind Turbines, Carleton College, 2005.

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