What this calculator does
Kinetic energy is the energy of motion and it depends on the square of speed, which is the single most important fact about it. Doubling speed does not double the energy, it quadruples it, and everything about braking distances and crash severity follows from that.
Potential energy is the energy of position: the energy stored by lifting a mass against gravity. This calculator gives both, and translates between them by reporting the fall height that would produce the same energy as the speed entered.
The formula
Kinetic energy is half the mass times the square of speed, with speed converted from kilometres per hour to metres per second first. Potential energy is mass times gravity times height. Equating the two gives the fall height that matches a given speed.
| Term | Meaning |
|---|---|
| Kinetic energy | The energy an object has because it is moving, proportional to the square of its speed. |
| Potential energy | The energy stored by raising a mass against gravity, proportional to height. |
| Joule (J) | The SI unit of energy. One joule is one newton acting over one metre. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the moving or raised object, in kilograms. |
| Speed (km/h) | The speed in kilometres per hour. It is converted to metres per second internally before squaring. |
| Height (m) | The height for the potential energy calculation, in metres. |
When to use it
Understanding why speed matters so much in a crash
The energy that has to be absorbed rises with the square of speed, so a modest increase in speed is a large increase in severity.
Comparing a fall with an impact
The equivalent fall height puts a driving speed into terms that are easier to picture: hitting something at speed is like dropping from a specific height.
Sizing energy storage or absorption
Anything that has to stop a moving mass, from a brake to a crash barrier, has to absorb its kinetic energy, so that figure is the design starting point.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does kinetic energy grow with speed for a 1,200 kg car?
The same car at a range of speeds.
| Speed | Kinetic energy | Equivalent fall height |
|---|---|---|
| 30 km/h | 41,667 J | 3.54 m |
| 50 km/h | 115,741 J | 9.84 m |
| 60 km/h | 166,667 J | 14.16 m |
| 100 km/h | 462,963 J | 39.34 m |
Questions
Why is speed squared but mass is not?
Because a faster object covers more distance in the same time while also pushing harder, and both effects scale with speed. The energy required therefore grows with speed twice over, while doubling the mass only doubles how much there is to move.
What does the equivalent fall height mean?
It is the height an object would have to be dropped from to reach the speed entered. It gives a physical sense of the energy involved: 50 km/h corresponds to a fall of roughly ten metres, or about a three-storey building.
Does kinetic energy depend on direction?
No. Energy is a scalar, so an object moving north at 50 km/h has exactly the same kinetic energy as one moving south at 50 km/h. Momentum, by contrast, does depend on direction.
Where does the energy go when something stops?
It is converted rather than destroyed, mostly into heat in the brakes or into deformation of whatever was struck. That is why brakes get hot and why crash structures are designed to crumple.
For the force and time behind a change in motion, see the momentum and impulse calculator. For how far a vehicle travels while stopping, see the acceleration and stopping distance calculator.