What kinetic energy is
Kinetic energy is the energy an object has because it's moving. It's the work needed to get it up to speed from rest, and the work it can do (or the damage it can cause) when it's brought back to a stop. Brakes turn a car's kinetic energy into heat; a hammer turns it into driving a nail.
The formula depends on mass and on the square of speed, so speed matters much more than mass. A car at 100 km/h carries four times the energy it has at 50 km/h.
The formula
m = 2 × KE ÷ v²
v = √(2 × KE ÷ m)
Use kilograms and meters per second to get joules. Conversions: 1 km/h = 1 ÷ 3.6 m/s, 1 mph = 0.44704 m/s, 1 lb = 0.45359237 kg, 1 ft·lbf = 1.355818 J, 1 kWh = 3,600,000 J.
Example: a 1,500 kg car at 100 km/h
How much kinetic energy does a 1,500 kg car carry at highway speed? These are the default values.
| Step | Result |
|---|---|
| Speed in m/s: 100 ÷ 3.6 | 27.78 m/s |
| Square it: 27.78² | 771.6 m²/s² |
| KE = ½ × 1,500 × 771.6 | 578,704 J (578.7 kJ) |
| In foot-pounds: 578,704 ÷ 1.355818 | 426,830 ft·lbf |
| In kWh: 578,704 ÷ 3,600,000 | 0.1608 kWh |
| Momentum: 1,500 × 27.78 | 41,667 kg·m/s |
That's the same energy as dropping the car from about 39 meters, roughly a 13-story building, which is why highway-speed crashes are so destructive.
Common mistakes
- Forgetting to square the speed. ½ × 1,500 × 27.78 gives momentum-like numbers, not energy.
- Using km/h or mph directly. Convert to m/s first or the answer will be off by a factor of 13 (km/h) or 5 (mph).
- Using grams. Mass must be in kilograms to get joules.
- Forgetting the ½. mv² without the half doubles the answer.
Frequently asked questions
What is the formula for kinetic energy?
KE = ½ × m × v², where m is the mass in kilograms and v is the speed in meters per second. The answer is in joules. A 2 kg ball moving at 3 m/s has ½ × 2 × 3² = 9 J of kinetic energy.
Why does doubling the speed quadruple the kinetic energy?
Because speed is squared in the formula. Going from 50 to 100 km/h multiplies v² by 4, so the car carries four times the energy, and needs roughly four times the distance to brake to a stop at the same deceleration.
What is a joule?
A joule is the SI unit of energy. It's the energy transferred when a force of 1 newton pushes something 1 meter. Lifting a small apple 1 meter takes about 1 joule. 1 kJ is 1,000 J, and 1 kWh is 3.6 million J.
How do I find velocity from kinetic energy?
Rearrange the formula: v = √(2 × KE ÷ m). For an object of 1,500 kg with 578,704 J of energy, v = √(2 × 578,704 ÷ 1,500) = 27.78 m/s, which is 100 km/h.
What is the difference between kinetic energy and momentum?
Both depend on mass and velocity, but momentum is m × v (a vector, with direction) and kinetic energy is ½mv² (a scalar). Momentum is always conserved in collisions; kinetic energy is often partly turned into heat, sound and bent metal.
Rates and figures last checked October 2026.
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