Calculate gravitational potential energy using PE = mgh. Includes height, mass solver, planetary comparison, and impact velocity.
The **Potential Energy Calculator** computes the gravitational potential energy of an object at a given height using the fundamental equation PE = mgh. It also solves for the required height or mass to achieve a target energy, and shows the impact velocity the object would have if dropped from that height.
Gravitational potential energy is one of the most fundamental concepts in physics — it represents stored energy due to an object's position in a gravitational field. A 1 kg mass held 10 meters above the ground stores 98.1 joules of energy (at Earth's surface gravity). Release it, and that energy converts entirely to kinetic energy just before impact, reaching a speed of 14 m/s (50 km/h).
This calculator goes beyond the basic formula by providing planetary comparisons (see how energy differs on the Moon, Mars, or Jupiter), a height-vs-energy table with visual bars, and energy equivalence in multiple units including kilocalories and kilowatt-hours. It supports a custom reference height, so you can calculate the energy relative to any elevation, not just the ground.
Understanding potential energy is essential for physics, engineering, and everyday safety analysis. Civil engineers calculate the potential energy of water in reservoirs to design hydroelectric dams. Safety engineers use it to assess fall hazard risks. Sports scientists analyze potential-to-kinetic energy conversion in skiing, diving, and roller coasters.
The planetary comparison feature makes this calculator uniquely useful for space science education, while the height-energy table helps visualize the quadratic relationship between height and impact severity.
Gravitational Potential Energy: PE = mgh Impact velocity (dropped): v = √(2gh) Energy equivalence: 1 J = 0.000239 kcal = 0.000278 Wh Variables: m = mass (kg), g = gravitational acceleration (m/s²), h = height above reference (m)
Result: 490.3 J
A 10 kg object at 5 m height: PE = 10 × 9.807 × 5 = 490.3 J. If dropped, it reaches v = √(2 × 9.807 × 5) = 9.90 m/s (35.6 km/h) just before impact. The same object on the Moon (g = 1.625 m/s²) would have only 81.25 J of potential energy.
Gravitational potential energy represents the work done against gravity to raise an object to a height h above a reference point. The formula PE = mgh emerges directly from the definition of work: the force (mg, the object's weight) multiplied by the displacement (h, the height). This stored energy is available to be converted back into kinetic energy whenever the object is released to fall.
The key insight is that potential energy is a property of the object's position in the gravitational field, not of its motion. Two objects at the same height with the same mass have the same PE regardless of how they got there. This path-independence is a hallmark of conservative forces and makes energy conservation calculations remarkably simple.
The principle of conservation of mechanical energy states that PE + KE = constant (in the absence of non-conservative forces like friction). This means a falling object converts potential energy to kinetic energy at every point in its descent. At height h, the velocity is v = √(2g(H-h)), where H is the starting height.
This principle underlies countless engineering systems: hydroelectric dams convert the PE of elevated water into electricity, regenerative braking converts KE back into stored energy, and pumped-storage facilities store energy by pumping water uphill during low-demand periods.
For applications involving large altitude changes (mountains, aircraft, spacecraft), the variation of g with altitude becomes significant. The general formula PE = -GMm/r accounts for this, where G is the gravitational constant, M is the planet's mass, and r is the distance from the planet's center. Near Earth's surface, this reduces to the familiar mgh with g = GM/R² = 9.807 m/s².
Not necessarily. Potential energy depends on the choice of reference point. If the object is below the reference height, PE is negative. Only differences in PE matter physically — the absolute value depends on the arbitrary reference.
No — gravitational potential energy depends only on the initial and final heights, not the path taken. This is because gravity is a conservative force. Whether an object is lifted straight up or carried up a ramp, the PE change is the same.
The impact velocity v = √(2gh) comes from energy conservation: mgh = ½mv². Mass cancels out on both sides. In vacuum (no air resistance), all objects fall at the same rate regardless of mass, as Galileo famously demonstrated.
The formula assumes constant g, which is valid near a planetary surface (within a few km of altitude). For very high altitudes (satellites, spacecraft), you need the general formula PE = -GMm/r, which accounts for the decrease in gravitational strength with distance.
In the absence of friction, total mechanical energy (PE + KE) is conserved. As an object falls, PE converts to KE. At the bottom, all PE has become KE: ½mv² = mgh, giving v = √(2gh).
Hydroelectric power (PE of water drives turbines), pumped-storage energy (pump water up to store energy), roller coaster design (initial height determines maximum speed), fall protection engineering (kinetic energy at impact), and crane load analysis (PE of lifted loads). Use this as a practical reminder before finalizing the result.