Definition of gravitational potential energy

Energy related to altitude

An object situated at a height possesses a form of energy related to its position within the gravitational field: this is gravitational potential energy, denoted Epp. It represents the work that the object’s weight could do if it were to fall back down to a reference level.

The formula

Epp = m * g * h

• m: mass of the object (in kg)
• g: acceleration due to gravity (approximately 9.8 N/kg on Earth, often rounded to 10 N/kg)
• h: height relative to a chosen reference level (in m)
• Epp: gravitational potential energy (in joules, J)

Choosing the reference level

Epp depends on a reference level (h = 0) which can be chosen freely: the ground, the ground floor, a table… Only the change in Epp between two positions has absolute physical meaning; the value of Epp itself depends on the arbitrary choice of this reference level.

Example

A book with mass m = 0.5 kg placed on a shelf at h = 1.5 m above the floor:

Epp = 0.5 * 10 * 1.5 = 7.5 J

Common pitfall

Do not confuse h, the height relative to the reference point, with the total distance travelled by the object. If the object moves horizontally, h does not change and Epp remains constant, even if the object has travelled a long distance.