Potential energy is energy stored by virtue of an object's position or configuration. Gravitational potential energy depends on height: PE = mgh. This calculator determines the energy an object possesses due to its elevation above a reference point, useful in engineering, physics problems, and energy analysis.
Gravitational potential energy: PE = mgh
A 70 kg person standing on a 10 m diving platform has a gravitational potential energy of 70 × 9.81 × 10 = 6867 J relative to the water surface. When they dive, this energy converts to kinetic energy. At the water surface, their speed is v = √(2gh) ≈ 14 m/s, confirming energy conservation.
Potential energy is always measured relative to a chosen reference level. The ground floor, sea level, or the bottom of a valley are common references. Only differences in potential energy are physically meaningful — the absolute value depends on the arbitrary reference.
PE = m × g × h
PE is potential energy in joules, m is mass in kg, g is gravitational acceleration (≈ 9.81 m/s²), and h is height above the reference point in metres.
PE = ½ × k × x²
Elastic potential energy stored in a spring, where k is the spring constant (N/m) and x is the displacement from equilibrium.
Energy conservation and practical applications
In a closed system, potential energy converts to kinetic energy and vice versa. A roller coaster at the top of a hill has maximum PE and minimum KE; at the bottom, PE is minimised and KE is maximised. Hydroelectric dams exploit gravitational PE by converting the energy of elevated water into electricity through turbines.
Pumped-storage hydropower stations pump water uphill during low-demand periods, storing energy as gravitational PE, then release it through turbines during peak demand. The round-trip efficiency is typically 70–85%.
Worked example and interpretation
A worked example helps translate the potential energy calculator maths into a realistic scenario so the user can compare the headline result with a concrete set of inputs.
That matters because a result is easier to trust when the page shows how the same logic behaves in a practical case instead of leaving the formula abstract.
Frequently asked questions
Does potential energy depend on the path taken?
No. Gravitational potential energy depends only on the vertical height difference, not the path. Whether you carry a box straight up a ladder or along a winding ramp to the same height, the change in PE is identical. This is because gravity is a conservative force.
Can potential energy be negative?
Yes. If the object is below the chosen reference level, its height h is negative, making PE negative. This is common in problems involving wells, valleys, or orbital mechanics. The sign is meaningful only relative to the reference point.
How is gravitational PE related to escape velocity?
Escape velocity is the speed at which an object's kinetic energy equals the magnitude of its gravitational potential energy relative to infinity. For Earth, this is about 11.2 km/s. At that speed, the object has enough energy to escape Earth's gravitational field entirely.
