Calculate gravitational potential energy with the formula PE = m · g · h. Enter any three of the four values — mass, gravitational acceleration, height, and potential energy — leave the fourth blank, and the calculator solves for it. Units are converted automatically.
The potential energy calculator works out the gravitational potential energy of an object — the energy it stores simply because of its position above a reference level. Lift a book onto a shelf, pump water into a tower, or haul a roller-coaster car to the top of the first hill, and you store energy that can be released later. This calculator uses the classic formula PE = m · g · h, and because it works in every direction, you can just as easily find the mass, the height, or the gravitational acceleration when you know the energy. Enter any three values, leave one blank, and get an accurate answer instantly, with flexible units throughout.
Potential energy is one of the cornerstones of physics, appearing everywhere from simple mechanics problems to hydroelectric power plants. This page explains what gravitational potential energy is, the formula behind it, worked examples you can reproduce, how the calculator handles each variable, and answers to the questions people ask most often.
Potential energy is stored energy — energy that an object holds because of its position or state, ready to be converted into other forms such as motion. The most familiar kind is gravitational potential energy, the energy an object has due to its height in a gravitational field. The higher you lift something, the more gravitational potential energy it gains, because gravity could do more work pulling it back down.
Energy is never created or destroyed, only transformed — this is the law of conservation of energy. When you lift an object, the work you do against gravity is stored as gravitational potential energy. Let the object fall, and that stored energy is released, converting into kinetic energy (the energy of motion) as it speeds up. This constant exchange between potential and kinetic energy drives everything from a swinging pendulum to a falling raindrop.
The formula for gravitational potential energy is beautifully simple:
PE = m × g × h
where:
In words: the potential energy equals the object's mass multiplied by the gravitational acceleration multiplied by its height. Double the height and you double the energy; double the mass and you double it again. The result comes out in joules, the SI unit of energy, where one joule is the energy needed to lift a small apple about one meter.
The value g = 9.81 m/s² is the acceleration that gravity gives to any falling object near the Earth's surface. It is the same for all masses — a feather and a hammer accelerate identically in a vacuum. The value varies slightly with location: it is a touch stronger at the poles and weaker at the equator and at high altitude. On other worlds it differs dramatically — about 1.62 m/s² on the Moon and 3.72 m/s² on Mars — so the calculator lets you change g to model gravitational potential energy anywhere.
Because the formula links four quantities, you can rearrange it to find whichever one you do not know. The calculator does this automatically — just leave one field blank:
This flexibility makes the tool useful for far more than a single calculation. You can work out how high an object must be raised to store a certain amount of energy, how much mass a given energy corresponds to, or even deduce the local gravity from a measured energy and position.
The default values in the calculator recreate a classic textbook example: an apple with a mass of 0.1 kg hanging at a height of 2.5 m. Using g = 9.81 m/s²:
PE = 0.1 kg × 9.81 m/s² × 2.5 m = 2.4525 J
So the apple stores about 2.4525 joules of gravitational potential energy. If the stalk breaks and the apple falls, that stored energy converts into kinetic energy, and the apple hits the ground with the same 2.4525 J of energy (ignoring air resistance). Press Calculate with the default values to see this result, then enter your own numbers.
Gravitational potential energy is always measured relative to a chosen reference level, most often the ground or floor. The height h in the formula is the distance above that reference. This means potential energy is not an absolute quantity — it depends on where you decide "zero height" is. A book on a second-floor shelf has more potential energy relative to the ground floor than relative to the second floor itself.
In practice, this rarely causes confusion, because what usually matters is the change in potential energy as an object moves up or down. When a ball falls from a height, only the drop in height determines how much energy is released, regardless of where you set the zero. Choose whatever reference level makes your problem simplest — the physics of the energy change stays the same.
Gravitational potential energy and kinetic energy are two sides of the same coin, and they constantly trade places. When an object falls, its height decreases, so its potential energy decreases — but it speeds up, so its kinetic energy increases by the same amount. At the moment just before impact, nearly all the original potential energy has become kinetic energy.
This is why an object dropped from height h reaches the ground with a speed given by combining the two energy formulas: setting m · g · h equal to ½ m · v² and solving gives v = √(2gh). Notice the mass cancels out, which is why all objects fall at the same rate. The interplay between potential and kinetic energy, with the total staying constant, is one of the most elegant results in classical mechanics and underlies the analysis of pendulums, projectiles, and orbits alike.
The SI unit of energy is the joule (J), and it is what the formula produces when mass is in kilograms, acceleration in m/s², and height in meters. For larger amounts, energy is often expressed in kilojoules (kJ) or megajoules (MJ); one kilojoule is 1,000 joules. Other common units include:
This calculator lets you read the potential energy in any of these units, converting automatically from joules so the result always makes sense for your context.
Because gravitational potential energy depends on g, the same object at the same height stores different amounts of energy on different planets. On the Moon, where g is only about 1.62 m/s², our 0.1 kg apple at 2.5 m would store just 0.405 J — roughly one-sixth of its energy on Earth. On Mars (g ≈ 3.72 m/s²) it would store about 0.93 J, and on Jupiter (g ≈ 24.79 m/s²) a hefty 6.2 J. By changing the gravitational acceleration in the calculator, you can explore how the same lift stores wildly different energy across the solar system — a vivid reminder that "weight" and stored gravitational energy are properties of the local gravitational field, not of the object alone.
While this calculator focuses on gravitational potential energy, it is worth knowing that potential energy comes in several forms. Elastic potential energy is stored in stretched or compressed objects like springs and rubber bands, given by ½ k · x², where k is the spring constant and x the deformation. Chemical potential energy is stored in the bonds of fuels and foods, and electric potential energy arises between charged objects. All of them share the same core idea: energy stored by virtue of position or configuration, waiting to be released. Gravitational potential energy is simply the most intuitive and widely encountered example, which is why it is the focus here.
PE = m × g × h, where m is mass (kg), g is gravitational acceleration (about 9.81 m/s² on Earth), and h is height (m). The result is in joules.
By default, g = 9.81 m/s², the standard gravitational acceleration at Earth's surface. You can change it to model other locations, such as 1.62 m/s² for the Moon or 3.72 m/s² for Mars.
Yes. The calculator is bidirectional — enter any three of the four values (mass, gravitational acceleration, height, potential energy) and leave the one you want blank, and it will solve for it.
Potential energy is stored energy due to position (such as height), while kinetic energy is the energy of motion. As an object falls, its potential energy converts into kinetic energy, keeping the total constant.
No. Gravitational potential energy depends only on the vertical height above the reference level, not on the route taken to get there. Climbing a winding path to a summit stores the same energy as going straight up.
The SI unit is the joule (J). The calculator can also display the result in kilojoules, megajoules, calories, kilocalories, watt-hours, kilowatt-hours, or foot-pounds.
This Potential Energy Calculator is provided for general educational and informational purposes. It computes gravitational potential energy using the standard formula PE = m·g·h and assumes a uniform gravitational field. For precise scientific or engineering work, account for local variations in gravity and other relevant factors.