Kinetic Energy Calculator
With mass 1500 kg, speed 27.78 m/s, friction coefficient 0.7, kinetic energy comes to 578,796 J — kinetic energy. It is reached in 8 steps, the last of which is 0.5 * 1500 * 27.78 * 27.78, and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Special Publication 811, not an approximation fitted to it.
Kinetic energy from mass and speed, with the stopping distance it implies — because the square on the velocity is the part that surprises people.
Formula and sources checked · How we check
Mass 1500 kg, Speed 27.78 m/s, Friction coefficient 0.7
578,796 J
Kinetic energy for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Kinetic energy — ½mv²
0.5 * 1500 * 27.78 * 27.78578,796.3 J- In kilojoules
578796.3 / 1000578.796 kJ- Momentum — mv
1500 * 27.7841,670 kg·m/s- Energy at twice this speed
0.5 * 1500 * pow(2 * 27.78, 2)2,315,185.2 J- Distance to stop, at this friction
578796.3 / (0.7 * 1500 * 9.80665)56.21 m- Distance to stop from twice the speed
2315185.2 / (0.7 * 1500 * 9.80665)224.841 m- The speed in km/h
27.78 * 3.6100.008 km/h- The speed in mph
27.78 / 0.4470462.142 mph
Worked example
A 1,500 kg car at 27.78 m/s — 100 km/h — carries 578,796 J, about 579 kJ. On dry asphalt that takes 56.2 m to shed. At twice the speed the energy is four times as large and the stopping distance is four times as long: 224.8 m, which is why a 20% overspeed is not a 20% problem.
How to work it out yourself
- 1.Use SI units or the answer is nonsense: kilograms and metres per second give joules. Pounds and miles per hour give a number with no unit at all.
- 2.Read the square. Kinetic energy goes as the velocity squared, so 10% more speed is 21% more energy and 21% more distance to stop. Every road safety argument about speed is this line.
- 3.The stopping distance here is the braking part only. Reaction time adds roughly the speed in metres per second times 1.5 seconds — about 42 m at 100 km/h — before the brakes do anything.
Energy and stopping distance by speed
| Speed (m/s) | Kinetic energy | Kinetic energy — ½mv² | Distance to stop, at this friction |
|---|---|---|---|
| 8.33 | 52,042 J | 52,041.68 J | 5.05 m |
| 13.4 | 134,670 J | 134,670 J | 13.08 m |
| 20 | 300,000 J | 300,000 J | 29.13 m |
| 27.78 | 578,796 J | 578,796.3 J | 56.21 m |
| 33.3 | 831,667 J | 831,667.5 J | 80.77 m |
| 44.4 | 1,478,520 J | 1,478,520 J | 143.59 m |
The formula
- Kinetic energy — ½mv²
0.5 * 1500 * 27.78 * 27.78 - In kilojoules
578796.3 / 1000 - Momentum — mv
1500 * 27.78 - Energy at twice this speed
0.5 * 1500 * pow(2 * 27.78, 2) - Distance to stop, at this friction
578796.3 / (0.7 * 1500 * 9.80665) - Distance to stop from twice the speed
2315185.2 / (0.7 * 1500 * 9.80665) - The speed in km/h
27.78 * 3.6 - The speed in mph
27.78 / 0.44704
Source: NIST Special Publication 811 — the joule and the units of energy, NHTSA — braking distance and the physics of stopping
Questions people actually ask
- What is the kinetic energy formula?
- KE = ½mv², with mass in kilograms and velocity in metres per second, giving joules. It comes from integrating force over distance for a constant acceleration, which is why the velocity appears squared and the mass does not.
- Why does doubling the speed quadruple the energy?
- Because the velocity is squared and 2² is 4. It has a physical meaning: the brakes remove energy at a roughly constant rate per metre, so four times the energy needs four times the distance. A car at 60 mph needs four times the braking distance of the same car at 30, not twice.
- What is the difference between kinetic energy and momentum?
- Momentum is mv and kinetic energy is ½mv². Momentum is conserved in every collision; kinetic energy is only conserved in an elastic one, and the difference is what crumples the car. A heavy slow lorry and a light fast car can share momentum and differ enormously in energy.
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