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Kinetic and potential energy: formulas and examples

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Kinetic energy is the energy an object has because it's moving. Gravitational potential energy is the energy stored because of its height. The two equations are:

Ek=12mv2Ep=mghE_k = \tfrac{1}{2} m v^2 \qquad E_p = m g h

with energy in joules, mass in kg, speed in m/s, gg in N/kg (about 9.8 on Earth) and height in metres. Check your answers with the kinetic energy and potential energy calculators.

Key takeaways

  • Kinetic energy = ½ × mass × speed².
  • Doubling speed quadruples kinetic energy.
  • GPE gained = mass × g × change in height.
  • In free fall, GPE lost = kinetic energy gained (ignoring air resistance).

Worked examples

  1. Kinetic energy: a 70 kg cyclist moves at 6 m/s. Ek=0.5×70×36=1,260E_k = 0.5 \times 70 \times 36 = 1{,}260 J.
  2. Potential energy: a 50 kg student climbs 3 m of stairs. Ep=50×9.8×3=1,470E_p = 50 \times 9.8 \times 3 = 1{,}470 J.
  3. Speed from energy: a 0.5 kg ball has 25 J of kinetic energy. v=2×25÷0.5=100=10v = \sqrt{2 \times 25 \div 0.5} = \sqrt{100} = 10 m/s.

Energy stores and transfers

GCSE courses describe energy as being in stores (kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear and more) and transferred between them by forces, heating, electric currents and waves. Energy is conserved: it isn't created or destroyed, but some is usually dissipated to the surroundings as thermal energy, which is wasted.

Falling objects

When an object falls freely, its gravitational potential energy is transferred to kinetic energy:

mgh=12mv2  ⇒  v=2ghmgh = \tfrac{1}{2}mv^2 \;\Rightarrow\; v = \sqrt{2gh}

A stone dropped from 20 m (with g=9.8g = 9.8 N/kg) lands at 392≈19.8\sqrt{392} \approx 19.8 m/s. Mass cancels out, so in a vacuum a feather and a hammer fall at the same rate. In air, air resistance means some energy goes to the surroundings and the speed is lower.

Work done

Work is done when a force moves an object:

W=F×dW = F \times d

(joules = newtons × metres, with the distance in the direction of the force). The work done is the energy transferred. Brakes do work on a car to remove its kinetic energy, which is why stopping distance increases sharply with speed: double the speed means four times the kinetic energy to remove.

Efficiency

efficiency=useful energy outputtotal energy input\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}

A motor that uses 500 J to lift a load and gives it 400 J of GPE is 400÷500=0.8400 \div 500 = 0.8, or 80%, efficient. The other 100 J is dissipated, mostly as thermal energy.

Common mistakes

  • Squaring the mass as well as the speed.
  • Forgetting the ½ in the kinetic energy equation.
  • Using the total height instead of the change in height for GPE.

Practice questions

  1. A 0.5 kg ball moves at 4 m/s. What is its kinetic energy?
  2. A 10 kg box is lifted 2 m (g = 9.8 N/kg). How much gravitational potential energy does it gain?
  3. An object is dropped from 5 m. Using g = 10 N/kg and ignoring air resistance, how fast is it moving when it lands?

Answers: 4 J; 196 J; 2×10×5=10\sqrt{2 \times 10 \times 5} = 10 m/s.

Frequently asked questions

How is kinetic energy linked to stopping distance?

Brakes must remove all of a vehicle's kinetic energy. Because kinetic energy depends on speed squared, the braking distance rises steeply as speed increases.

What is the difference between kinetic and potential energy?

Kinetic energy is energy of movement. Gravitational potential energy is energy stored because of an object's height in a gravitational field.

What is the unit of energy?

The joule (J). One joule is the energy transferred when a force of 1 newton moves an object 1 metre.

What is the kinetic energy formula?

Eₖ = ½mv²: half × mass (kg) × speed (m/s) squared, giving joules.

Why does kinetic energy depend on speed squared?

Because of how the work done to accelerate an object builds up. In practice it means doubling the speed gives four times the kinetic energy.

Is energy lost when an object falls?

Not destroyed. Some is transferred to the surroundings by air resistance, which heats the air slightly, so less ends up as kinetic energy.

Sources

  1. GCSE Physics (8463) specification: subject content. AQA.
  2. Cambridge IGCSE Physics 0625 syllabus for 2026, 2027 and 2028. Cambridge International.

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