A book sitting on a shelf, water held behind a dam, a roller coaster paused at its highest point: these are all examples of gravitational potential energy. Any object that has mass and is elevated above a reference point stores energy simply because gravity could pull it down. The higher and heavier the object, the more energy it holds. This energy is calculated with a straightforward formula: mass × gravity × height, measured in joules.
How the Formula Works
Gravitational potential energy equals mass times the acceleration due to gravity times height, written as PE = mgh. On Earth, gravity accelerates objects at 9.8 meters per second squared. So a 5-kilogram bowling ball sitting on a 2-meter-high table stores about 98 joules of potential energy (5 × 9.8 × 2). Double the height, and you double the stored energy. Double the mass, same thing.
One important detail: height is always measured relative to some reference point you choose. That reference point is where potential energy equals zero. For a ball on a table, you’d typically set the floor as zero. For a skydiver, you’d use the ground. The actual number you get for potential energy only has meaning as a difference between two positions, so picking a consistent reference level matters more than which level you pick.
Water Behind a Dam
One of the most practical, large-scale examples is a hydroelectric dam. Water accumulates in a reservoir high above the turbines at the base of the dam. That elevated water stores enormous gravitational potential energy. When gates open and water rushes downhill through channels called sluices, that stored energy converts into the spinning motion of turbine blades, which generates electricity. The U.S. Geological Survey notes that a hydroelectric system’s capacity depends on two things: how much water flows and how far it falls. A taller dam with a deeper reservoir stores more gravitational potential energy per gallon of water, which is why hydroelectric dams are built in mountainous terrain with steep elevation drops.
A Roller Coaster at Its Peak
Roller coasters are a textbook example because they make the energy conversion so visible. A motor hauls the coaster car up the first and tallest hill. At the top, the car is barely moving but packed with gravitational potential energy. As it drops, that potential energy converts directly into kinetic energy (the energy of motion), and the car accelerates. At the bottom of the hill, nearly all the potential energy has become speed.
The physics here leads to a surprising result: when friction is small enough to ignore, the coaster’s speed at the bottom depends only on how far it fell, not on the shape of the track or the mass of the car. A coaster dropping 20 meters straight down reaches the same speed as one that spirals and curves through that same 20-meter height change. That’s because the equation simplifies neatly. The loss in potential energy (mgh) equals the gain in kinetic energy (½mv²), and the mass cancels out on both sides, leaving speed determined by height alone.
Weights in a Grandfather Clock
Mechanical grandfather clocks run entirely on gravitational potential energy. Inside the case, heavy weights hang from chains wrapped around a drum. When you wind the clock, you’re pulling those weights upward, storing energy. Over the following days, the weights sink slowly as gravity pulls them down, and that gradual release of energy drives the gears, the pendulum, and the hands on the face. The pendulum acts as a regulator, allowing the escapement mechanism to release one tiny increment of stored energy per swing, which is what produces the clock’s steady tick.
Eventually the weights reach the bottom of the case and the clock stops. Winding it again lifts the weights and restores their potential energy. Ancient water clocks worked on the same principle: elevated water descended under gravity to turn gears. Grandfather clocks simply replaced water with metal weights for a cleaner, more reliable energy source.
A Pile Driver on a Construction Site
Pile drivers pound steel or concrete columns deep into the ground to create foundations for buildings and bridges. The basic mechanism is pure gravitational potential energy. A heavy ram, sometimes weighing several tons, is raised to a set height (called the stroke) by a hydraulic system or cable. Then it’s released. The ram free-falls under gravity, and all that stored potential energy converts to kinetic energy just before it strikes the top of the pile, driving it into the soil. The higher the stroke and the heavier the ram, the more energy delivered per blow. Some diesel-powered versions add a combustion boost at the bottom of the stroke to launch the ram back up for the next cycle, but the core energy source is the same: mass lifted against gravity.
Why Gravity Matters in the Equation
The “g” in the formula isn’t the same everywhere. On Earth’s surface it’s 9.8 m/s², but on the Moon it’s roughly 1.6 m/s², about one-sixth as strong. That means a 10-kilogram rock lifted 3 meters on Earth stores 294 joules of potential energy, while the same rock at the same height on the Moon stores only about 48 joules. The object’s mass and height haven’t changed, but the weaker gravitational pull means less energy is stored. This is why lunar vehicles need far less energy to climb hills than earthbound ones, and why engineers designing equipment for different planetary bodies have to recalculate energy budgets from scratch.
Everyday Examples You Already Know
- A raised hammer: Lifting a hammer above a nail stores energy. The swing converts it to kinetic energy right before impact.
- A child at the top of a slide: All potential energy at the top, all kinetic energy at the bottom.
- A skier at a mountaintop: Elevation above the base lodge represents stored energy that will become speed on the way down.
- Fruit on a tree: An apple hanging from a branch has more gravitational potential energy than one already on the ground. The moment it detaches, that energy begins converting to motion.
- A drawn bow with an arrow (indirectly): While the bow itself stores elastic energy, the archer’s arm raised the bow and arrow against gravity. The arrow’s height contributes gravitational potential energy to its total energy in flight.
In every case, the pattern is identical. Something with mass is elevated above a lower position. Gravity is ready to pull it down. The energy waiting to be released is gravitational potential energy, and its size is determined by three things: how heavy the object is, how strong gravity is, and how high it sits.