About kinetic energy
Kinetic energy is the energy an object has because it is moving. The faster it goes and the more mass it carries, the more kinetic energy it stores. Formally it is the work needed to accelerate an object of mass m from rest to a speed v, and it is released again when the object is brought back to rest. This calculator takes a mass in kilograms and a speed in metres per second and returns the kinetic energy in joules, with conversions to kilojoules and food calories.
The defining feature of the formula is that speed enters squared. Doubling the mass doubles the kinetic energy, but doubling the speed quadruples it. This single fact explains why crash severity rises so sharply with speed: a car at 60 mph carries four times the kinetic energy it had at 30 mph, and all of that energy must be dissipated in the collision. It is also why a light bullet can be lethal: a small mass multiplied by an enormous squared velocity yields a large energy.
Kinetic energy is a scalar, so it has magnitude but no direction; a car going north and one going south at the same speed have the same kinetic energy. It is always measured relative to a frame of reference, almost always the ground. The joule, its SI unit, equals one kilogram metre-squared per second-squared, the same unit used for every other form of energy, which is what lets kinetic energy convert into heat, sound, and deformation during an impact.
How it works: the formula
Kinetic energy is one-half the mass times the speed squared. Keep mass in kilograms and speed in metres per second to get joules directly.
KE = (1/2) x m x v^2 KE = kinetic energy in joules (J) m = mass in kilograms (kg) v = speed in metres per second (m/s) Rearranged: v = sqrt(2 x KE / m) m = 2 x KE / v^2
- The one-half comes from integrating force over distance (work) as the object accelerates; it is not arbitrary.
- The square on v means kinetic energy is far more sensitive to speed than to mass. Triple the speed and energy rises nine-fold.
- Units must be SI. If you have grams or km/h, convert first: divide grams by 1000, and divide km/h by 3.6 to get m/s.
- The formula is the non-relativistic (classical) form, accurate for everyday speeds well below the speed of light.
Worked example
Take the calculator's defaults: a 10 kg object moving at 5 m/s.
- Square the speed: v^2 = 5 x 5 = 25 m2/s2.
- Multiply by mass: 10 kg x 25 = 250.
- Apply the one-half: KE = 0.5 x 250 = 125 J.
- Now double the speed to 10 m/s: KE = 0.5 x 10 x 100 = 500 J, four times as much.
- Convert: 125 J is 0.125 kJ, or about 0.030 food calories (kcal).
Reference table: everyday kinetic energies
Approximate kinetic energy of common objects, computed as one-half mass times speed squared.
| Object | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Thrown baseball | 0.145 kg | 40 m/s (90 mph) | 116 J |
| Sprinting human | 70 kg | 10 m/s | 3,500 J |
| Cyclist | 90 kg | 8 m/s | 2,880 J |
| Car at 30 mph | 1,500 kg | 13.4 m/s | 134,700 J |
| Car at 60 mph | 1,500 kg | 26.8 m/s | 538,800 J |
| 9mm bullet | 0.008 kg | 360 m/s | 518 J |
Common pitfalls
- Forgetting that speed is squared. The single most common error is assuming kinetic energy scales linearly with speed. It does not; the energy at 40 mph is far more than double the energy at 20 mph.
- Mixing units. Entering speed in km/h or mph, or mass in grams or pounds, breaks the joule output. Convert to kilograms and metres per second first.
- Confusing kinetic energy with momentum. Momentum is mass times velocity (a vector) and is conserved in collisions; kinetic energy is one-half mass times speed squared (a scalar) and is only conserved in perfectly elastic collisions.
- Ignoring the reference frame. Kinetic energy is always relative to an observer. A passenger has zero kinetic energy relative to the train but a large value relative to the platform.
- Treating it as the only energy. A real moving object may also have rotational kinetic energy (a spinning wheel) and potential energy (height). This formula gives only the translational kinetic energy of the centre of mass.
Frequently asked questions
What is the formula for kinetic energy?
Kinetic energy equals one-half times mass times velocity squared, written KE = 0.5 x m x v^2. With mass in kilograms and velocity in metres per second, the result is in joules. The factor of one-half arises from integrating force over the distance needed to accelerate the object from rest to its final speed.
Why does kinetic energy increase with the square of speed?
Because the work done to accelerate an object grows with both the force and the distance, and at constant acceleration the distance covered scales with the square of the final speed. The result is that doubling speed quadruples kinetic energy and tripling it raises the energy nine-fold. This is why stopping distances and crash severity climb so steeply with speed.
What units does kinetic energy use?
The SI unit is the joule (J), equal to one kilogram metre-squared per second-squared. To get joules directly, enter mass in kilograms and speed in metres per second. If your inputs are in grams, pounds, km/h, or mph, convert them to SI units first, since the formula assumes consistent SI quantities.
What is the difference between kinetic energy and momentum?
Momentum is mass times velocity, a vector that points in the direction of motion and is conserved in every collision. Kinetic energy is one-half mass times speed squared, a scalar with no direction that is conserved only in perfectly elastic collisions. The squared term means kinetic energy weights speed much more heavily than momentum does.
Can kinetic energy be negative?
No. Mass is always positive and the square of velocity is never negative, so kinetic energy is always zero or positive. It is zero only when the object is at rest relative to the chosen reference frame. A change in kinetic energy can be negative, which simply means the object slowed down and lost energy.