Gravitational Potential Energy

The Bath County pumped-storage station in Virginia has two reservoirs separated by 380 meters of elevation. At night, cheap electricity pumps water uphill. During peak demand, the water flows back down through turbines, generating up to 3 GW. The "battery" is gravity. The stored energy is in the height.

Gravitational potential energy is the energy an object possesses by virtue of its position in a gravitational field: PE = mgh, where m is mass (kg), g is gravitational acceleration (9.8 m/s²), and h is height above a reference point (m). The formula says three things matter: more mass, more height, or stronger gravity all increase stored energy.

This is the physics behind hydroelectric power, the world's largest source of renewable electricity. Water at the top of a dam has potential energy proportional to its mass and the height it can fall. When released through a turbine, gravity converts that potential energy to kinetic energy, and the turbine converts kinetic energy to electricity.

Worked Example

A pumped-storage facility lifts 1,000,000 kg of water (about 1,000 cubic meters) to a height of 200 meters.

• Apply PE = mgh. PE = 1,000,000 kg x 9.8 m/s² x 200 m = 1.96 x 10⁹ J = 1,960 MJ.
• Convert to kWh. 1,960 MJ / 3.6 MJ per kWh = 544 kWh.

If the round-trip efficiency (pump up, generate down) is 80%, how much electricity is recovered?

544 x 0.80 = 435 kWh. The 20% loss goes to friction, turbulence, and heat. Pumped hydro is the oldest and largest form of grid-scale energy storage, and gravitational PE is its entire operating principle.

This same equation applies to any falling object: water, rock, a roller coaster, or a construction crane's payload.

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