Kinetic Energy Calculator

GCSE PhysicsAQAEdexcelOCRFoundation & Higher

Find kinetic energy, mass or speed using Ek = ½ m v². Enter what you know in any units. You'll get the answer and every line of working, ready to copy into your book.

Quick answer

Kinetic energy = 0.5 × mass × speed². Use mass in kg and speed in m/s to get joules (J). For example, a 2 kg ball moving at 3 m/s has Ek = 0.5 × 2 × 3² = 9 J.

By Mehmood Kakar · Updated

Ek = ½ × m × v²
Find:

How to calculate kinetic energy

Kinetic energy is the energy an object has because it is moving. On your equation sheet it is written as:

kinetic energy = 0.5 × mass × (speed)²

  • Ek is kinetic energy in joules (J)
  • m is mass in kilograms (kg)
  • v is speed in metres per second (m/s)

In an exam, set out every calculation in the same four steps: write the equation, convert units, substitute the numbers, then give the answer with its unit. Even if your final number is wrong, examiners can award marks for a correct substitution.

Common mistakes that cost marks

  1. Forgetting to square the speed. Only v is squared, not the whole ½ × m × v.
  2. Leaving mass in grams. 500 g is 0.5 kg. Using 500 makes your answer 1000 times too big.
  3. Leaving speed in km/h. Divide by 3.6 to get m/s: 72 km/h = 20 m/s.
  4. Missing the square root. When you find speed, the last step is √. Check: does your speed look sensible?
  5. Rounding too early. Keep the full value until the end, then round (usually to 2 or 3 significant figures).
  6. No unit on the answer. Kinetic energy is in J. Some mark schemes give a mark for the unit.

Practice questions

Try each one on paper first, then reveal the worked answer.

Q1A car of mass 1200 kg travels at 15 m/s. Calculate its kinetic energy.[2 marks]
  1. Ek = ½ × m × v²
  2. Ek = 0.5 × 1200 × 15²
  3. 15² = 225, so Ek = 0.5 × 1200 × 225
  4. Ek = 135 000 J (135 kJ)
Q2A tennis ball of mass 60 g has 27 J of kinetic energy. Calculate its speed.[3 marks]
  1. Convert: m = 60 g ÷ 1000 = 0.06 kg
  2. Rearrange: v = √(2 × Ek ÷ m)
  3. v = √(2 × 27 ÷ 0.06) = √900
  4. v = 30 m/s
Q3A runner moving at 8.0 m/s has 2240 J of kinetic energy. Calculate the runner’s mass.[3 marks]
  1. Rearrange: m = 2 × Ek ÷ v²
  2. m = (2 × 2240) ÷ 8.0²
  3. m = 4480 ÷ 64
  4. m = 70 kg

Frequently asked questions

What is the kinetic energy equation for GCSE Physics?

Kinetic energy = 0.5 × mass × (speed)², written Ek = ½mv². Kinetic energy is in joules (J), mass in kilograms (kg) and speed in metres per second (m/s).

Is the kinetic energy equation on the GCSE equation sheet?

Yes. For AQA GCSE Physics (8463) and Combined Science, every physics equation, including kinetic energy, is printed on the equation sheet you get in the exam. The skill being tested is choosing it, rearranging it and using the right units.

How do you rearrange Ek = ½mv² to find speed?

Multiply both sides by 2, divide by the mass, then take the square root: v = √(2Ek ÷ m). Forgetting the square root is the most common mistake.

What units must I use?

Mass in kg and speed in m/s gives kinetic energy in J. Convert grams to kilograms (÷ 1000) and km/h to m/s (÷ 3.6) before you substitute.