Kinetic energy is the energy an object has because it is moving: KE = ½mv², with mass in kilograms and speed in meters per second giving energy in joules. A 1,500 kg car traveling at 25 m/s (about 56 mph) carries ½ × 1,500 × 25² = 468,750 J. Because speed is squared, doubling the speed quadruples the energy.
The kinetic energy formula
| Symbol | Quantity | SI unit |
|---|---|---|
| KE | Kinetic energy | joule (J) |
| m | Mass | kilogram (kg) |
| v | Speed | meter per second (m/s) |
One joule is the energy of a 2 kg mass moving at 1 m/s, or the work done by a force of 1 newton over 1 meter. It is a small amount: lifting an apple about a meter takes roughly 1 J.
Steps
- Convert mass to kilograms and speed to meters per second.
- Square the speed.
- Multiply by the mass, then by ½.
Car: m = 1,500 kg, v = 25 m/s
v² = 625 → KE = ½ × 1,500 × 625 = 468,750 J (about 469 kJ)
Baseball: m = 0.145 kg, v = 40 m/s (about 89 mph)
KE = ½ × 0.145 × 1,600 = 116 J
The kinetic energy calculator solves for energy, mass or speed and handles unit conversions such as mph and pounds.
Why speed matters more than mass
Mass enters the formula once; speed enters twice.
| Car at… | Speed | Kinetic energy | Relative to 25 m/s |
|---|---|---|---|
| 12.5 m/s | 28 mph | 117,188 J | ¼ |
| 25 m/s | 56 mph | 468,750 J | 1 |
| 37.5 m/s | 84 mph | 1,054,688 J | 2¼ |
| 50 m/s | 112 mph | 1,875,000 J | 4 |
Brakes must remove all of that energy as heat. With the same braking force, stopping distance is proportional to kinetic energy, so it also grows with the square of speed. This is the physics behind the braking-distance results in kinematic equations explained.
Kinetic energy of everyday things
| Object | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Person walking | 70 kg | 1.4 m/s | about 69 J |
| Thrown baseball | 0.145 kg | 40 m/s | 116 J |
| Cyclist and bike | 85 kg | 7 m/s (25 km/h) | about 2,080 J |
| Rifle bullet | 8 g | 900 m/s | 3,240 J |
| Car | 1,500 kg | 25 m/s | 468,750 J |
| Loaded truck | 30,000 kg | 25 m/s | 9,375,000 J |
The bullet has about 1/190,000 of the car’s mass, yet carries about 0.7% of its energy, entirely because of its speed. The truck, at the same speed as the car, carries twenty times the energy because it has twenty times the mass, which is why heavy vehicles need so much more room to stop.
Solving for speed or mass
A 0.145 kg ball has 116 J: v = √(2 × 116 ÷ 0.145) = √1,600 = 40 m/s
Gravitational potential energy
Potential energy is stored energy. Lifting an object against gravity stores energy that is released when it falls:
Here g ≈ 9.81 m/s² near Earth’s surface and h is the height above a chosen reference level.
A 2.0 kg book lifted onto a 1.5 m shelf: PE = 2.0 × 9.81 × 1.5 ≈ 29.4 J
Only changes in height matter, so you can measure h from the floor, the table or any convenient level, as long as you are consistent. The potential energy calculator handles other planets’ gravity too.
Trading potential for kinetic energy
Without friction or air resistance, mechanical energy is conserved: potential energy lost equals kinetic energy gained.
Mass cancels, so every object dropped from the same height reaches the same speed (ignoring air).
A roller coaster drops 40 m from rest
v = √(2 × 9.81 × 40) = √784.8 ≈ 28.0 m/s (about 63 mph) at the bottom
A real coaster arrives a bit slower because friction and air drag convert some energy to heat. The same equation gives the impact speed in the free fall calculator.
Elastic potential energy
A stretched or compressed spring stores energy too:
A spring with stiffness k = 200 N/m compressed by 0.10 m stores ½ × 200 × 0.01 = 1.0 J. See the elastic potential energy calculator.
Work and the work-energy theorem
Work is force times distance in the direction of motion, W = F × d. The work-energy theorem says the net work done on an object equals its change in kinetic energy. To stop the 468,750 J car in 50 meters, the brakes must supply an average force of 468,750 ÷ 50 = 9,375 N. The work calculator covers force, distance and angle.
Energy unit conversions
| Unit | Joules | Example |
|---|---|---|
| 1 kilojoule (kJ) | 1,000 | |
| 1 food Calorie (kcal) | 4,184 | Nutrition labels |
| 1 British thermal unit (BTU) | about 1,055 | Heating and cooling |
| 1 watt-hour (Wh) | 3,600 | Batteries |
| 1 kilowatt-hour (kWh) | 3,600,000 | Electric bills |
Power is the rate at which energy is delivered. Bringing the car from rest to 25 m/s in 10 seconds requires an average of 468,750 ÷ 10 = 46,875 W at the wheels, about 63 horsepower, before counting drag and drivetrain losses. The car’s 468,750 J is about 0.13 kWh or 112 food Calories, which shows how much energy is tied up in motion compared with everyday electrical use. The energy converter converts between these and many more.
Common mistakes
- Using km/h or mph directly. Convert to m/s first: divide km/h by 3.6, or multiply mph by 0.44704.
- Using grams. Mass must be in kilograms for joules.
- Forgetting to square the speed, or squaring the whole product ½mv.
- Dropping the ½.
A note on relativity
KE = ½mv² is extremely accurate for everyday speeds. Near the speed of light it fails, and Einstein’s relativistic formula takes over, in which energy grows without limit as speed approaches c. The related rest-energy relation E = mc² is explored in the E = mc² calculator.
Frequently asked questions
What is the formula for kinetic energy?
KE = ½mv², where m is mass in kilograms and v is speed in meters per second. The result is in joules. A 1,500 kg car moving at 25 m/s has ½ × 1,500 × 25² = 468,750 J of kinetic energy.
What happens to kinetic energy when speed doubles?
It quadruples, because speed is squared. A car at 50 m/s has four times the kinetic energy of the same car at 25 m/s, and needs roughly four times the distance to stop with the same braking force.
How do you find speed from kinetic energy?
Rearrange the formula: v = √(2 × KE ÷ m). A 0.145 kg baseball with 116 J of kinetic energy is moving at √(2 × 116 ÷ 0.145) = 40 m/s.
What is the difference between kinetic and potential energy?
Kinetic energy is energy of motion. Potential energy is stored energy due to position or configuration, such as height in a gravitational field (mgh) or a stretched spring (½kx²). In a falling object, potential energy converts to kinetic energy.
Can kinetic energy be negative?
No. Mass is positive and speed is squared, so kinetic energy is always zero or positive, no matter which direction the object moves.