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Kinetic Energy Calculator and Formula

The kinetic energy formula is Ek = ½mv²: kinetic energy = 0.5 × mass × (speed)², with mass in kg, speed in m/s and kinetic energy in joules (J). Doubling the speed makes the kinetic energy four times as large.

Kinetic energy formula: Ek = ½mv²

Ek = m·v²2
Ek = m·v²2m = 2·Ekv²v = 2·Ekm
Ek
kinetic energy, J
m
mass, kg
v
speed, m/s

Convert every value to SI units (m, s, kg, A, V, Ω) before substituting into the formula. The calculator does this for you and shows the conversion as a step.

240 kJ
Ekkinetic energy
240 kJ
kinetic energy: 240 kJ
A trolley of mass 1200 kg moves at 20 m/s, and the bar shows its kinetic energy, 240000 J. The faded bar shows that at twice the speed the kinetic energy would be four times as large.

Step-by-step solution

  1. FormulaEk = m·v²2
  2. In SI unitsv = 72 km/h = 20 m/s
  3. SubstituteEk = 1200 kg · (20 m/s)²2
  4. AnswerEk = 240000 J = 240 kJ

Kinetic energy examples

  1. Example 1

    A ball of mass 0.5 kg rolls across the floor at 4 m/s. Calculate its kinetic energy in joules.

    Given:m = 0.5 kgv = 4 m/s
    1. FormulaEk = m·v²2
    2. SubstituteEk = 0.5 kg · (4 m/s)²2
    3. AnswerEk = 4 J

  2. Example 2

    A sledge carrying a small child slides down a hill at 10 m/s and has 1000 J of kinetic energy. Calculate the total mass of the sledge and child.

    Given:Ek = 1000 Jv = 10 m/s
    1. Formulam = 2·Ekv²
    2. Substitutem = 2 · 1000 J(10 m/s)²
    3. Answerm = 20 kg

  3. Example 3

    A car of mass 1200 kg has 240 kJ of kinetic energy. Calculate its speed in m/s.

    Given:Ek = 240 kJm = 1200 kg
    1. Formulav = 2·Ekm
    2. In SI unitsEk = 240 kJ = 240000 J
    3. Substitutev = 2 · 240000 J1200 kg
    4. Answerv = 20 m/s

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What is kinetic energy?

Kinetic energy is the energy an object has because it is moving. At GCSE the equation is kinetic energy = 0.5 × mass × (speed)², written Ek = ½mv², with mass in kilograms, speed in metres per second and energy in joules. Anything that moves has energy in its kinetic store, from a rolling ball to a lorry on the motorway.

Speed is squared, so it matters far more than mass. Double the mass and the kinetic energy doubles; double the speed and the kinetic energy becomes four times as large. That is why braking distance rises so steeply with speed: the brakes have to transfer all of that energy away, mostly by heating the brake discs.

Kinetic energy is never negative and depends only on speed, not on direction. In energy questions it often appears alongside gravitational potential energy: as a ball falls, energy is transferred from its gravitational potential energy store to its kinetic energy store.

Common mistakes

  • Forgetting to square the speed, or squaring ½mv instead of just v.
  • Leaving the speed in km/h. Convert to m/s first by dividing by 3.6, or the answer will be far too large.
  • Using grams or tonnes instead of kilograms: 250 g is 0.25 kg and 1.5 t is 1500 kg.
  • Forgetting the square root when finding speed: v = √(2Ek/m), not 2Ek/m.
  • Missing out the ½: mv² on its own is twice the kinetic energy.

Related formulas

Speed, distance and timeEfficiencyAccelerationAll physics equations

Frequently asked questions

Kinetic energy = 0.5 × mass × (speed)², or Ek = ½mv². Use mass in kg and speed in m/s to get the energy in joules.

It becomes four times as large, because the speed is squared. Tripling the speed makes it nine times as large.

Rearrange the formula to v = √(2Ek/m): multiply the kinetic energy by 2, divide by the mass, then take the square root.

The joule, J. Larger values are often given in kilojoules (1 kJ = 1000 J) or megajoules (1 MJ = 1000 kJ).

No. Mass is positive and the square of the speed is never negative, so kinetic energy is zero for an object at rest and positive for anything that is moving.