Introduction
Potential energy is the energy an object has because of its position or height. When you hold a ball above the ground, it stores energy that can turn into motion once you let go. The formula to find potential energy is simple: PE = m × g × h, where m is mass, g is gravitational acceleration, and h is height. This relationship means that heavier objects, stronger gravity, and greater heights all lead to more stored energy.
Our Potential Energy Calculator lets you solve for any variable in the formula — whether you need to find the energy, mass, gravity, or height. Just enter the values you know, pick your units, and get your answer right away. The calculator converts between units like kilograms, pounds, meters, and feet automatically. It also shows a step-by-step solution so you can follow the math and learn as you go. You can even compare two objects side by side, explore gravity on different planets like Mars or the Moon, and see related values like velocity at impact and power required. Try one of the built-in example scenarios or plug in your own numbers to get started.
How to Use Our Potential Energy Calculator
Enter the mass, gravity, and height of an object, and this calculator will give you its gravitational potential energy using the formula PE = m × g × h. You can also solve for any other variable in the equation.
What would you like to calculate: Use the dropdown menu to pick which value you want to find. You can solve for potential energy, mass, gravity, or height. The calculator will adjust its input fields based on your choice.
Example Scenarios: If you want to see the calculator in action right away, click one of the preset examples — a person on a ladder, a ball on a roof, or water in a dam. These will fill in the input fields for you automatically.
Mass (m): Enter the mass of the object. You can pick your preferred unit from the dropdown, including kilograms, grams, metric tons, pounds, and ounces.
Gravity (g): Enter the gravitational acceleration value. It defaults to 9.81 m/s² for Earth. You can also click the quick-select buttons to use gravity values for the Moon, Mars, or Jupiter. The unit can be set to m/s² or ft/s². For deeper exploration of gravitational interactions between objects, try our Gravitational Force Calculator.
Height (h): Enter the vertical height of the object above your chosen reference point. Choose from meters, kilometers, centimeters, feet, inches, yards, or miles.
Potential Energy (PE): This field appears when you are solving for mass, gravity, or height instead of energy. Enter the known potential energy value and select your unit, such as joules, kilojoules, calories, kilocalories, BTU, or kilowatt-hours.
Time (optional): If you want to know how much power is needed to lift the object to the given height, enter a time value in seconds, minutes, or hours. This is not required for the main calculation.
Enable Comparison Mode: Check this box to compare two objects side by side. A second set of fields will appear where you can enter the mass, gravity, and height for a second object. The results will show both energy values and the percentage difference between them.
Calculate: Once all required fields are filled in, click the "Calculate" button. The calculator will display your result, a step-by-step solution, the velocity and kinetic energy at impact, work done, power required (if time is entered), fun energy equivalents, and a graph of potential energy versus height.
What Is Potential Energy?
Potential energy is the energy an object has because of its position or height above the ground. Think of it this way: when you lift a book onto a shelf, you are giving that book energy. The higher you place it, the more energy it stores. This stored energy is called gravitational potential energy, and it can be turned into motion (kinetic energy) if the object falls.
The Potential Energy Formula
The formula for gravitational potential energy is:
PE = m × g × h
- PE = potential energy, measured in joules (J)
- m = mass of the object, measured in kilograms (kg)
- g = gravitational acceleration, measured in meters per second squared (m/s²)
- h = height above a reference point, measured in meters (m)
On Earth, the value of g is approximately 9.81 m/s². This number changes depending on which planet or moon you are on. For example, the Moon's gravity is only 1.62 m/s², so the same object at the same height would have much less potential energy on the Moon than on Earth. You can use our G Force Calculator to explore how gravitational acceleration affects objects in different contexts.
How Potential Energy Works in Real Life
Potential energy is everywhere in daily life. A roller coaster at the top of a hill has a large amount of potential energy. As it rolls downhill, that potential energy converts into kinetic energy, which is the energy of motion. A glass sitting on a table has potential energy relative to the floor. Water held behind a dam stores enormous potential energy that can be used to generate electricity in hydroelectric power plants.
The Relationship Between Potential and Kinetic Energy
One of the most important ideas in physics is the conservation of energy. This means energy is never created or destroyed — it just changes form. When an object falls freely (ignoring air resistance), all of its potential energy at the top converts into kinetic energy at the bottom. This relationship gives us a useful equation for finding the speed of an object just before it hits the ground:
v = √(2 × g × h)
This means that a heavier object and a lighter object dropped from the same height will hit the ground at the same speed, but the heavier object will carry more kinetic energy because it has more mass. You can verify this using our Free Fall Calculator, which computes the time and velocity of freely falling objects.
Rearranging the Formula
You can rearrange the potential energy formula to solve for any variable you need:
- To find mass: m = PE ÷ (g × h)
- To find height: h = PE ÷ (m × g)
- To find gravity: g = PE ÷ (m × h)
This is helpful when you already know the energy of an object and need to figure out one of the other values. For instance, if you know how much energy a falling rock releases on impact, you can work backward to find the height it fell from. If you're working with forces rather than energy, our Force Calculator can help you determine the net force acting on an object.
Potential Energy and Power
If you know how quickly energy is used or transferred, you can also calculate power. Power is simply energy divided by time:
P = PE ÷ t
Power is measured in watts (W). For example, if a crane lifts a 500 kg load to a height of 20 meters in 10 seconds, you can first calculate the potential energy (98,100 J) and then divide by 10 seconds to find the crane uses 9,810 watts of power. For automotive and mechanical applications, our Horsepower Calculator can convert between watts and horsepower.
Why Understanding Potential Energy Matters
Engineers use potential energy calculations to design bridges, buildings, dams, and safety systems. Athletes and coaches use it to understand the physics of jumping and throwing. Scientists use it to study everything from falling raindrops to orbiting satellites. By understanding this simple formula, you gain a powerful tool for explaining how energy is stored and released in the world around you. To explore related mechanical concepts, check out our Momentum Calculator, Impulse Calculator, or Projectile Motion Calculator. For energy at the atomic scale, Einstein's famous equation can be explored with our E = mc² Calculator.