β¬οΈ Potential Energy Calculator
PE = mgh β Calculate gravitational potential energy or solve for any variable.
Result
How to Use This Calculator
Select whether you want to find potential energy, mass, or height, then fill in the other three values. The gravity field g defaults to 9.81 m/sΒ² for Earth but you can change it. Height is measured from whatever reference level you choose (usually the floor or ground level).
Select what to solve for: Potential Energy (J), Mass (kg), or Height (m) from the dropdown.
Enter mass in kilograms. A 70 kg person, a 5 kg dumbbell, a 2000 kg car β use whatever your problem states.
Enter height in metres above the reference level you have chosen. The reference is arbitrary: set h = 0 wherever it is most convenient for your problem.
Adjust g for other planets if needed: Moon = 1.62, Mars = 3.72, Jupiter = 24.79 m/sΒ².
Potential Energy Formula
Gravitational PE is always measured relative to a chosen reference height. Only changes in PE matter physically. If you set the ground as h = 0, then lifting a 10 kg box to a shelf at 1.5 m gives PE = 10 Γ 9.81 Γ 1.5 = 147.15 J. That energy came from the muscles doing work and is stored waiting to be released if the box falls.
Worked Examples
Where This Comes Up in Real Life
Hydroelectric power stations convert the gravitational potential energy of water stored at height into electricity. A dam holding 10 million kg of water at 100 m has PE = 10β· Γ 9.81 Γ 100 = 9.81 Γ 10βΉ J = 9.81 GJ. Converting this to kilowatt-hours (1 kWh = 3.6 MJ) gives about 2,725 kWh. Even accounting for efficiency losses of 10-20%, that is a substantial energy return from gravity alone.
Roller coaster design uses PE and KE conversion constantly. If the first hill is 40 m high and the car starts from rest, the maximum speed at the bottom (ignoring friction) is v = β(2gh) = β(2 Γ 9.81 Γ 40) = 28 m/s, about 100 km/h. Engineers then work backward from desired maximum speeds and safety margins to determine what height every subsequent hill must be, since no hill after the first can be taller than the starting drop without adding a motor.
Frequently Asked Questions
What is gravitational potential energy?
It is the energy stored in an object due to its position relative to a reference height. PE = mgh, where m is mass (kg), g is gravitational acceleration (m/sΒ²), and h is height (m).
What is the standard value of g?
On Earth's surface: g β 9.81 m/sΒ². On the Moon: 1.62 m/sΒ². On Mars: 3.72 m/sΒ². Use 9.81 for most calculations.
What is the reference height?
PE is relative β you choose the reference (h=0). Common choices: ground level, table surface, or lowest point of motion.
How is PE related to KE?
In a conservative system: PE + KE = constant (conservation of energy). Falling objects convert PE to KE.
What is the unit of potential energy?
Joules (J) in SI. 1 J = 1 kgΒ·mΒ²/sΒ². Also expressed in kJ for larger values.