### Table of Contents

- Definition
- Formula
- Vehicle example
- Bullet example
- Calculator
- Kinetic energies for various objects
- References

### 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.

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.

### 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]:

_{k}= (m · v

^{2}) / 2

where:

- E
_{k}[J] – kinetic energy - m [kg] – mass
- v [m/s] – speed

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

### 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:

**Step 2**. Calculate the kinetic energy E_{k} [J] of the vehicle using equation (1):

_{k}= (m · v

^{2}) / 2 = (1200 · 34.72

^{2}) / 2 = 723287.04 J

### 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:

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

**Step 3**. Calculate the kinetic energy E_{k} [J] of the bullet using equation (1):

_{k}= (m · v

^{2}) / 2 = (0.03 · 792.44

^{2}) / 2 = 9419.42 J

### 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.

### Kinetic energies for various objects

Object | Mass [kg] | Speed [m/s] | Kinetic energy [J] |
---|---|---|---|

Earth orbiting the Sun | 5.98·10^{24} | 2.98·10^{4} | 2.65·10^{33} |

Moon orbiting the Earth | 7.35·10^{22} | 1.02·10^{3} | 3.82·10^{23} |

Rocket moving at escape speed^{a} | 500 | 1.12·10^{4} | 3.14·10^{10} |

Automobile at 55 miles per hour | 2000 | 25 | 6.3·10^{5} |

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.

### 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.