Easily calculate the kinetic energy of an object in motion such as a bullet or an arrow. Metric and imperial measurement units with output in Joules (J, kJ, MJ), Watt-hours (Wh, kWh), calories (Cal, kCal), and foot-pounds (ft-lbs). The calculator can also be used to solve for mass or velocity.

Quick navigation:

- Using the kinetic energy calculator
- Kinetic energy formula
- Kinetic energy calculation examples

## Using the kinetic energy calculator

This **kinetic energy calculator** is useful for estimating the energy a body acquires through movement of any kind. For example, it can be used to calculate the kinetic energy of a person, vehicle (car, truck, train), plane, football, as well as for falling bodies that crash into the ground. It can also be used to calculate the energy of different kinds of projectiles: bullets, arrows, kinetic shells. To calculate the kinetic energy you need to know only the body's mass and velocity. Its acceleration does not matter since the energy is calculated at a particular moment of time.

The KE calculator can also be used to **solve for any of the other values: mass and velocity**. The respective input fields will be hidden or displayed upon selecting what you want to use the calculator for. When solving for mass you need to know velocity and kinetic energy, while when solving for velocity you need to know the object's mass and kinetic energy.

The output of the tool if calculating for kinetic energy is in Joules (J, kJ, MJ), Watt-hours (Wh, kWh), calories (Cal, kCal) and foot-pounds (ft-lbs). When the output of the tool is mass or velocity it is in both standard metric units and imperial ones, with the units automatically being adjusted depending on how big or small the resulting value is.

## Kinetic energy formula

In physics, the formula for kinetic energy (**KE**) expressed in terms of the body's velocity (speed) (**v**) and its mass (**m**) is the equation:

This equation is used in coding this online kinetic energy calculator and it shows the relationship between mass and energy is mediated through velocity. A body with a given mass has a higher kinetic energy if it has a higher velocity, and vice versa. The formula also shows that a body with a larger mass will have a larger kinetic energy at a certain velocity. It should be noted that velocity has exponential impact on energy, whereas mass has a linear impact, which has implication for ways to generate energy, such as in increasing one's punching power.

The KE formula and the equations below are valid in classical mechanics and for non-rotating rigid point objects (the object's mass is assumed to exist at a single point). If the object's speed is larger than a couple of percentages of the speed of light in vacuum it is a poor approximation according to relativistic mechanics.

### Calculate mass given KE and velocity

Solving for mass requires a simple reordering of the equation:

### Calculate velocity given KE and mass

Alternatively, one can solve for velocity and calculate it using the formula:

in which "KE" is kinetic energy and *m* is mass.

## Kinetic energy calculation examples

*Example 1:* A **car** weighs 2200kg (2.2 tonnes) and is moving with a velocity of 40 km/h. What is the car's kinetic energy? To calculate the kinetic energy, first convert km/h to meters per second: 40km/h = 11.11 m/s. Using the first kinetic energy equation above, replace the values for m and v and get KE = 2200 · (11.11)^{2} / 2 = 135775.3 Joules or 135.7753 kiloJoules.

*Example 2:* A ball which weighs 500 grams has a kinetic energy of 500 J. What is the velocity of the ball? First we convert 500 grams to 0.5 kg and then replace in the formula: v = √(2 · 500 / 0.5) = 44.7214 m/s or 146.7236 feet per second.

*Example 3:* A plane is moving at a speed of 800 km/h and it has kinetic energy of 2100 MJ (MegaJoules). What is the plane's mass? First we need to convert MJ to J: 2,100 · 1,000,000 = 2,100,000,000 J. Then we need to convert 800 km/h to m/s which is 222.22(2) m/s. Finally we replace in the formula to get m = 2 · 2,100,000,000 / 222.22^{2} = 85,050 kg = 85.05 tonnes.

*Example 4:* A .50 caliber bullet leaves the muzzle of a sniper rifle with a velocity of 3,000 feet per second and has a known mass of 52 grams. What is the bullet's kinetic energy? Begin by converting feet per second to meters per second, for which we need to convert feet to meters. A foot is 0.3048 meters, so 3,000 ft/s equals 3,000 * 0.3048 = 914.4 meters per second. 52 grams equals 0.052 kg. Replacing m and v in the formula we get KE = 0.052 · (914.4)^{2} / 2 = 21.7393 kJ or about 16,034 ft-lbs for the kinetic energy of the bullet.

Of course, while using our calculator you would not need to perform these unit conversions, as they are handled for you on the fly.

### Ton vs tonne, tons vs tonnes

When solving for the object's mass we output both tonne (metric ton) and ton (short ton). The first one is used by all countries in the world and is defined to be equal to 1000 kg by the international body of standardization. The ton is currently only used in the United States and is equal to 2000 pounds (2000 lbs).

#### References

1 NIST Special Publication 330 (2008) - "The International System of Units (SI)", edited by Barry N.Taylor and Ambler Thompson, p. 52

2 "The International System of Units" (SI) (2006, 8th ed.). *Bureau international des poids et mesures* pp. 142–143. ISBN 92-822-2213-6