Calculate gravitational potential energy, mass, or height using PE = m × g × h.
📂 PhysicsFill in the fields on the left with your circuit's known values, then press the button to see your result instantly. No sign-up required, and no data is sent anywhere — everything is calculated right in your browser.
Gravitational potential energy is the energy stored in an object due to its position at a certain height within a gravitational field, calculated by the equation PE = m × g × h, where m is the object's mass, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth's surface), and h is the object's height above a reference point (usually the ground). Potential energy's SI unit is the joule (J), the same unit as kinetic energy, since the two can convert into one another — as happens when an object falls from a certain height, where potential energy gradually converts to kinetic energy while the total mechanical energy (assuming no air resistance or friction) stays constant throughout the fall. This calculator lets you find any one of the three quantities (energy, mass, or height) with the option to adjust the gravity value g for calculations on other planets or under different gravitational conditions. This concept is used in designing hydroelectric dams, elevators, and pumped-storage energy systems, where height differences are deliberately engineered to store and release large amounts of energy on demand.
Gravitational potential energy captures a genuinely useful physical idea: raising an object against gravity requires doing work against that gravitational pull, and that invested work doesn't disappear — it's stored in the object's elevated position, ready to be released as the object falls back down.
This stored-and-released energy relationship is exactly why potential energy and kinetic energy share the same unit (the joule) and convert so cleanly between each other: an object at height h has potential energy mgh and zero kinetic energy at rest, but as it falls, that potential energy steadily converts into kinetic energy, with the total (assuming no air resistance) remaining exactly constant throughout the fall — a clean demonstration of the broader law of conservation of mechanical energy.
Hydroelectric power generation is essentially industrial-scale gravitational potential energy conversion: a dam holds water at height behind it, representing enormous stored potential energy across the mass of water involved, and releasing that water through turbines converts the potential energy into kinetic energy (moving water) and then into electrical energy as the turbines spin generators.
Pumped-storage hydroelectric systems take this a step further as a genuine large-scale energy storage technology: during periods of excess electricity supply (such as overnight when demand is low), these systems use that surplus electrical energy to pump water uphill into an elevated reservoir, deliberately converting electrical energy into stored gravitational potential energy. Later, during periods of high electricity demand, that stored water is released back downhill through turbines, converting the potential energy back into electricity exactly when it's needed — making pumped storage one of the most mature and widely deployed grid-scale energy storage technologies precisely because it exploits this simple gravitational relationship at a massive scale.
Elevator design also directly grapples with gravitational potential energy: a loaded elevator car gains substantial potential energy as it rises, and well-designed elevator systems use counterweights (which fall as the car rises, and vice versa) specifically to reduce the net energy the motor must supply, since the counterweight's changing potential energy partially offsets the car's, making the overall system significantly more energy-efficient than lifting the full car weight against gravity without any counterbalancing mechanism.
Height is measured relative to whatever reference point you choose (commonly the ground or the lowest point of motion) — potential energy is always relative, not absolute.
Standard Earth gravity (9.81 m/s²) is the default, but the formula works the same way for other gravitational accelerations, such as the Moon's (~1.62 m/s²) or Mars' (~3.71 m/s²).
In the absence of friction or air resistance, potential energy converts into kinetic energy as an object falls, following the principle of conservation of mechanical energy (their sum stays constant).