Potential Energy Calculator — Physics
Calculate gravitational potential energy (PE = mgh), elastic potential energy (PE = ½kx²), or solve for mass, height, and spring constant with step-by-step solutions. Includes gravity presets for all planets. 100% private — runs in your browser.
How Potential Energy Calculations Work
Potential energy is stored energy based on an object's position or configuration. The two most common forms are gravitational potential energy and elastic potential energy. Gravitational PE depends on an object's mass, height above a reference point, and the local gravitational field strength. The formula PE = mgh gives the energy in joules when mass is in kilograms, gravity in m/s², and height in meters.
Elastic potential energy is stored in a compressed or stretched spring. It follows the formula PE = ½kx², where k is the spring constant in newtons per meter and x is the displacement from the equilibrium position. This relationship comes from Hooke's Law, which states that the restoring force of a spring is proportional to its displacement.
Gravitational vs Elastic Potential Energy
Gravitational potential energy applies to any object with mass at a height above a reference plane. It increases linearly with both mass and height — doubling the height doubles the stored energy. This form of PE is central to problems involving falling objects, roller coasters, pendulums, and hydroelectric dams.
Elastic potential energy, on the other hand, depends on the square of the displacement. Doubling the stretch of a spring quadruples the stored energy. This makes elastic PE particularly important in engineering applications like vehicle suspension systems, archery bows, and mechanical watches. Unlike gravitational PE, elastic PE is always positive regardless of direction because displacement is squared.
Energy Conservation Principle
The conservation of energy states that energy cannot be created or destroyed — only transformed from one form to another. When an object falls, its gravitational potential energy converts to kinetic energy. At the highest point of a throw, kinetic energy is zero and potential energy is maximum. At ground level, potential energy is zero and kinetic energy is maximum. This principle lets you calculate velocity at any height: v = √(2gh), derived by setting mgh equal to ½mv².
In spring systems, elastic potential energy converts to kinetic energy when the spring is released. A compressed spring in a toy car stores elastic PE that becomes kinetic energy as the car moves forward. Energy conservation applies in both ideal and real-world scenarios, though friction and air resistance convert some energy to heat.
Potential Energy Applications
Gravitational potential energy calculations are used in civil engineering to design dams and water towers, in aerospace engineering to compute orbital mechanics, and in sports science to analyze jumping and diving. Elastic potential energy is critical in mechanical engineering for shock absorbers, in materials science for stress-strain analysis, and in biomedical engineering for prosthetic limb design. Understanding both forms of potential energy is essential for physics students studying mechanics, thermodynamics, and energy systems.