Gravitational potential energy calculator (Eₚ = mgh)

On Earth, $g$ is about 9.8 N/kg, which is the value AQA gives in its exams. Some questions use 10 N/kg to keep the numbers simple, so always use the value your question or data sheet gives. On the Moon, $g$ is about 1.6 N/kg.

• Energy: a 2 kg bag is lifted 5 m. $E_p = 2 \times 9.8 \times 5 = 98$ J.
• Height: a 5 kg mass gains 490 J. $h = 490 \div (5 \times 9.8) = 10$ m.
• Mass: lifting an object 4 m gives it 200 J (with $g = 10$ N/kg). $m = 200 \div (10 \times 4) = 5$ kg.

When an object falls freely, the GPE it loses becomes kinetic energy (ignoring air resistance):

Dropped from 5 m with $g = 9.8$ N/kg, an object lands at $\sqrt{98} \approx 9.9$ m/s, whatever its mass. Try it with the kinetic energy calculator.

GCSE courses describe energy in stores: lifting something increases its gravitational potential energy store; as it falls, energy is transferred to its kinetic store. Air resistance means some energy is dissipated to the thermal store of the surroundings, so the real speed is a little lower than the calculation suggests.

• Using the total height above the ground when the question asks for the change in height.
• Mixing grams and kilograms.
• Forgetting that the answer is in joules; divide by 1,000 for kJ.

See kinetic energy explained for more on energy transfers.