Kinetic Energy: formula
Enter the mass in kilograms and the speed in meters per second. Kinetic energy is half the mass times the speed squared, in joules, and momentum is mass times speed. Convert miles per hour by dividing by 2.237 and kilometers per hour by dividing by 3.6.
The result is also shown in kilowatt-hours to put it in energy-bill terms.
Kinetic Energy: worked example
| Mass (kg) | 1,500 |
|---|---|
| Speed (m/s) | 25 |
| Kinetic energy (joules) | 468,750 |
| Kinetic energy (kWh) | 0.13 |
| Momentum (kg·m/s) | 37,500 |
The formula covers translational energy of a rigid body. Rotating parts such as wheels store additional energy. At very high speeds near light, relativistic formulas apply.
Real collisions dissipate energy as heat and deformation, so it is not simply conserved in the vehicles.
Kinetic Energy: changing Mass (kg)
| Mass (kg) | Kinetic energy (joules) | Kinetic energy (kWh) | Momentum (kg·m/s) |
|---|---|---|---|
| 1,200 | 375,000 | 0.104 | 30,000 |
| 1,350 | 421,875 | 0.117 | 33,750 |
| 1,500 (example) | 468,750 | 0.13 | 37,500 |
| 1,650 | 515,625 | 0.143 | 41,250 |
| 1,800 | 562,500 | 0.156 | 45,000 |
Kinetic Energy: compare input ranges
| Input | Tested from | To | Kinetic energy (joules): low input | Kinetic energy (joules): high input | Swing |
|---|---|---|---|---|---|
| Speed (m/s) | 23 | 28 | 396,750 | 588,000 | 191,250 (41%) |
| Mass (kg) | 1,350 | 1,650 | 421,875 | 515,625 | 93,750 (20%) |
Kinetic Energy: individual input comparisons
| Input | Value | Kinetic energy (joules) | Kinetic energy (kWh) | Momentum (kg·m/s) |
|---|---|---|---|---|
| Mass (kg) | 1,200 | 375,000 | 0.104 | 30,000 |
| 1,350 | 421,875 | 0.117 | 33,750 | |
| 1,500 | 468,750 | 0.13 | 37,500 | |
| 1,650 | 515,625 | 0.143 | 41,250 | |
| 1,800 | 562,500 | 0.156 | 45,000 | |
| Speed (m/s) | 20 | 300,000 | 0.083 | 30,000 |
| 23 | 396,750 | 0.11 | 34,500 | |
| 25 | 468,750 | 0.13 | 37,500 | |
| 28 | 588,000 | 0.163 | 42,000 | |
| 30 | 675,000 | 0.188 | 45,000 |
Kinetic Energy: combined input changes
| Mass (kg) / Speed (m/s) | 20 | 25 | 30 |
|---|---|---|---|
| 1,200 | 240,000 | 375,000 | 540,000 |
| 1,350 | 270,000 | 421,875 | 607,500 |
| 1,500 | 300,000 | 468,750 | 675,000 |
| 1,650 | 330,000 | 515,625 | 742,500 |
| 1,800 | 360,000 | 562,500 | 810,000 |
Kinetic Energy: which assumptions move the result?
Kinetic Energy: values and definitions
| Quantity and definition | Value used |
|---|---|
| Mass (kg) | 1,500 |
| Speed (m/s) — 25 meters per second is about 56 miles per hour. | 25 |
| Kinetic energy (joules) | 468,750 |
| Kinetic energy (kWh) | 0.13 |
| Momentum (kg·m/s) | 37,500 |
Kinetic Energy: half and double Speed (m/s)
| Speed (m/s) | Kinetic energy (joules) |
|---|---|
| 12.5 | 117,187.5 |
| 25 | 468,750 |
| 50 | 1,875,000 |
Common error: Doubling the energy for double the speed. Doubling speed at unchanged mass multiplies modeled kinetic energy by four. Collision injury depends on additional circumstances.
Physics & Mechanics calculators: Newton's Second Law Force Calculator, Uniform Acceleration Calculator, Hooke's Law Calculator, Ideal Gas Law Calculator, Gravitational Potential Energy Calculator, Work and Power Calculator.
Kinetic energy grows with the square of speed, so a small rise in speed adds a lot of energy. A 1,500 kilogram car at 25 meters per second, about 56 miles an hour, carries 468,750 joules. At double that speed the energy quadruples.
That is the reason braking distance and crash severity climb so quickly, and why speed matters more than weight.
The exact international-mile conversion is 0.44704 meters per second per mile per hour, commonly rounded to 0.447. A speed of 36 km/h equals 10 m/s, while 20 mph equals 8.9408 m/s. The squared-speed term makes a mistaken unit conversion affect energy twice through multiplication.
See the force on the force calculator, the fall and impact speed on the free fall calculator and the height energy on the potential energy calculator. The work and power and centripetal force pages cover related mechanics, and the horsepower calculator relates energy to engines.
What does momentum measure here?
The mass times the velocity, a measure of how hard an object is to stop, in kilogram meters per second.
How do you calculate kinetic energy?
Multiply half the mass by the square of the speed, giving energy in joules when the mass is in kilograms and speed in meters per second.
Why does speed matter so much in a crash?
Kinetic energy grows with the square of speed, so doubling the speed makes the crash energy four times as large.