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Free Kinetic Energy Calculator

This kinetic energy calculator finds the energy of a moving object from its mass and speed using the equation KE = ½ x m x v². Enter the mass in kilograms and the velocity in metres per second, and the tool returns the kinetic energy in both joules and kilojoules, along with the object's linear momentum (p = m x v). Kinetic energy is the energy an object possesses because of its motion, and it is central to problems in mechanics, vehicle safety, sports physics and engineering whenever you need to know how much work was done to set something moving or how much energy it would release on impact.

Enter mass and velocity to find kinetic energy.

Result
Kinetic energy300,000 J
Kinetic energy300 kJ
Momentum (p = m·v)30,000 kg·m/s

KE = ½ · m · v² · p = m · v. Use SI units: kilograms and metres per second. Divide km/h by 3.6 to get m/s.

Quick answer

Kinetic energy is the energy of motion, calculated as KE = ½ x m x v², where m is mass in kilograms and v is speed in metres per second. The result is in joules (J): one joule equals one kg·m²/s². For example, a 1500 kg car at 20 m/s has KE = ½ x 1500 x 20² = 300,000 J (300 kJ). Because velocity is squared, doubling the speed quadruples the kinetic energy.

Formula & method

Kinetic energy

KE = ½ · m · v²
  • KE — kinetic energy in joules (J)
  • m — mass in kilograms (kg)
  • v — speed (magnitude of velocity) in metres per second (m/s)

One joule = 1 kg·m²/s². Divide joules by 1000 to get kilojoules (kJ). Use the object's speed, not its direction; KE is always positive.

Momentum (also shown)

p = m · v
  • p — linear momentum in kg·m/s
  • m — mass in kilograms (kg)
  • v — velocity in metres per second (m/s)

Momentum scales linearly with speed, whereas kinetic energy scales with the square of speed. The two are related by KE = p² / (2m).

Examples

Example 1: Kinetic energy of a small car
Input
m = 1000 kg, v = 10 m/s
Result
KE = 50,000 J = 50 kJ, p = 10,000 kg·m/s
Why
KE = ½ x m x v² = 0.5 x 1000 x 10² = 0.5 x 1000 x 100 = 50,000 joules, which is 50 kJ. Momentum is p = m x v = 1000 x 10 = 10,000 kg·m/s. At 10 m/s (36 km/h) a one-tonne car already carries enough energy to do serious damage on impact.
Example 2: A thrown baseball
Input
m = 0.145 kg, v = 40 m/s
Result
KE = 116 J, p = 5.8 kg·m/s
Why
KE = ½ x m x v² = 0.5 x 0.145 x 40² = 0.5 x 0.145 x 1600 = 116 joules. Momentum is p = m x v = 0.145 x 40 = 5.8 kg·m/s. A regulation baseball (about 145 g) pitched at roughly 90 mph carries on the order of 100 joules of kinetic energy.
Example 3: Why doubling speed quadruples energy
Input
m = 2 kg at v = 3 m/s, then at v = 6 m/s
Result
9 J → 36 J (4× the energy)
Why
At 3 m/s: KE = 0.5 x 2 x 3² = 0.5 x 2 x 9 = 9 joules. At 6 m/s: KE = 0.5 x 2 x 6² = 0.5 x 2 x 36 = 36 joules. Doubling the speed multiplied the kinetic energy by four (36 ÷ 9 = 4), because velocity is squared in the formula. Momentum only doubled, from 6 to 12 kg·m/s.
Example 4: Default example: a mid-size car at speed
Input
m = 1500 kg, v = 20 m/s
Result
KE = 300,000 J = 300 kJ, p = 30,000 kg·m/s
Why
KE = ½ x m x v² = 0.5 x 1500 x 20² = 0.5 x 1500 x 400 = 300,000 joules, i.e. 300 kJ. Momentum is p = m x v = 1500 x 20 = 30,000 kg·m/s. At 20 m/s (72 km/h) a 1.5-tonne car stores about 300 kJ, roughly the energy released by burning a tenth of a gram of petrol.

When to use this tool

  • Estimating the impact energy of a vehicle, projectile or falling object at a known speed and mass for safety or design analysis.
  • Solving introductory physics and engineering homework involving the work–energy theorem, where work done equals the change in kinetic energy.
  • Comparing how a change in speed affects energy, for example showing students that going from 30 to 60 km/h quadruples the energy that brakes must dissipate.
  • Sanity-checking momentum and energy together in collision or recoil problems before applying conservation laws.

Common mistakes

  • Forgetting to square the velocity. KE = ½ x m x v² means you square v first, then multiply by mass and a half. Multiplying by v just once (½ x m x v) gives a wrong, far smaller number.
  • Using km/h instead of m/s. The joule is defined in SI units, so speed must be in metres per second. Convert km/h to m/s by dividing by 3.6 (e.g. 72 km/h ÷ 3.6 = 20 m/s) before entering it.
  • Entering mass in grams or pounds. Mass must be in kilograms for the answer to come out in joules. Divide grams by 1000 (145 g = 0.145 kg) and multiply pounds by 0.4536 to get kilograms.
  • Confusing kinetic energy with momentum. They are different quantities: KE = ½mv² (in joules) measures energy and depends on v², while momentum p = mv (in kg·m/s) is linear in v. Doubling speed quadruples KE but only doubles momentum.

Frequently asked questions

What is the formula for kinetic energy?

The kinetic energy of a moving object is KE = ½ x m x v², where m is the mass in kilograms and v is the speed in metres per second. The result is in joules. The half and the squared velocity come from integrating force over distance (the work–energy theorem): the work needed to accelerate a mass from rest to speed v equals ½mv².

What units does this calculator use?

It uses SI units: mass in kilograms (kg) and velocity in metres per second (m/s), giving kinetic energy in joules (J) and, for convenience, in kilojoules (kJ). One joule equals one kg·m²/s². If your data is in km/h, grams or pounds, convert first: divide km/h by 3.6, divide grams by 1000, and multiply pounds by 0.4536.

Why does doubling the speed quadruple the kinetic energy?

Because velocity is squared in KE = ½mv². If you double v, then v² becomes four times larger, so the kinetic energy increases by a factor of four for the same mass. This is why stopping distances and crash energy rise so sharply with speed: a car at 60 km/h carries four times the kinetic energy it had at 30 km/h.

What is the difference between kinetic energy and momentum?

Kinetic energy (½mv², measured in joules) is a scalar that describes the energy of motion and grows with the square of speed. Momentum (p = mv, measured in kg·m/s) is a vector that grows linearly with speed. Energy tells you how much work the object can do or how much heat a collision releases; momentum tells you how hard it is to stop and is conserved in collisions. They are linked by KE = p² / (2m).

Can kinetic energy be negative?

No. Mass is always positive and velocity is squared, so v² is positive regardless of direction. That makes kinetic energy always zero or positive: it is zero only when the object is at rest. Direction does not matter for kinetic energy, which is why we use speed (the magnitude of velocity) rather than a signed velocity in the formula.

Does this formula work at very high speeds?

The KE = ½mv² formula is the classical (Newtonian) result and is extremely accurate for everyday speeds. It only breaks down as an object approaches the speed of light, where Einstein's relativistic energy formula is needed. For cars, balls, bullets and almost all engineering problems, the classical formula used here is essentially exact.

Sources & references

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