Potential Energy Calculator

Potential energy is energy stored because of position or configuration. Unlike kinetic energy, which depends on motion, potential energy depends on the relationship between an object and a force field or on deformation within a system. This calculator covers two standard introductory-physics models: gravitational potential energy near a planetary surface and elastic potential energy in an ideal linear spring. Both results are expressed in joules. Near Earth's surface, gravitational potential energy relative to a chosen reference height is U = mgh. Here m is mass in kilograms, g is gravitational acceleration in metres per second squared, and h is vertical height in metres. The default g value of 9.81 m/s² is a common Earth approximation. Potential energy is relative, so h is measured from whatever zero level is useful for the problem. Only differences in potential energy affect motion; changing the reference adds the same constant to all positions without changing physical predictions. The constant-gravity expression works when the height change is small compared with the planet's radius. For satellites, interplanetary problems, or very large altitude changes, use the universal gravitational potential U = -GMm/r instead. Local gravitational acceleration also varies slightly with latitude and elevation. You can replace the default value for the Moon, Mars, another body, or a more precise local calculation. An ideal spring stores elastic energy U = ½kx², where k is spring constant in newtons per metre and x is displacement from the relaxed equilibrium length in metres. Squaring displacement means equal compression and extension store the same energy in the ideal model. The equation follows by integrating the Hooke's-law force F = kx from zero displacement to x. It applies only while the spring remains linear and elastic; real springs can show preload, hysteresis, coil contact, yielding, or nonlinear stiffness. Energy conservation often converts potential energy into kinetic, thermal, acoustic, or deformation energy. A falling object can ideally gain kinetic energy equal to its lost gravitational potential energy, while a released spring can accelerate an attached mass. Real systems dissipate some mechanical energy through drag, friction, damping, and internal losses. Use this calculator for homework, laboratory planning, quick design estimates, and energy comparisons. For safety-critical lifting or spring systems, account for efficiency, dynamic impact, material limits, fatigue, and an appropriate design factor.