Potential Energy Calculator
PE = m × g × h — height and gravity
Quick planet presets:
Quick presets:
Enter Your Values
Select a PE type tab, enter mass, height, and gravity (or spring constant and displacement), then see your potential energy result with step-by-step solution and real-world energy comparison.
How to Use the Potential Energy Calculator
Choose the PE Type
Select the tab that matches your problem: Gravitational (mgh) for objects lifted in a gravity field, Elastic (½kx²) for springs and elastic materials, or Electric (k_e q₁q₂/r) for charged particle systems. Each tab shows only the inputs relevant to that formula.
Select What to Solve For
Use the 'Solve for' dropdown to choose your unknown variable. For Gravitational PE you can solve for energy, mass, height, or gravity. For Elastic PE you can solve for energy, spring constant k, or displacement x. For Electric PE you can solve for energy, either charge, or the separation distance r.
Enter Known Values with Units
Type your known values into the visible input fields. Use the unit dropdowns beside each field to match your measurement system — mass can be in kg, g, lb, or oz; height in m, cm, ft, or inches. For gravitational calculations, click a planet button to auto-fill the correct gravity for Earth, Moon, Mars, Jupiter, and more.
Read the Results and Context
Your answer appears instantly in the result card. Expand 'Step-by-Step Solution' to see the full worked derivation. Scroll down to the Energy Context chart to compare your result against everyday energy references — from lifting an apple (≈1 J) to consuming 1 kWh of electricity (3,600,000 J). All ten energy units are shown simultaneously in the conversions table.
Frequently Asked Questions
What is the formula for gravitational potential energy?
The formula for gravitational potential energy is PE = m × g × h, where m is the mass in kilograms, g is the gravitational acceleration in meters per second squared (9.81 m/s² on Earth), and h is the height above the chosen reference point in meters. The result is in joules. This formula assumes a uniform gravitational field, which is valid for heights well below Earth's orbital altitudes. On other planets, simply substitute the appropriate surface gravity — for example, g = 1.62 m/s² on the Moon, giving objects far less stored energy at the same height than on Earth.
What does a negative electric potential energy mean?
A negative electric potential energy means the two charges have opposite signs — one positive and one negative — and are in a bound, attractive system. In physics, the reference point for electric PE is infinity: two charges infinitely far apart have zero PE. When opposite charges are brought closer, the system loses energy (work is done by the attractive force), so the PE becomes negative. A negative electric PE indicates that energy must be supplied to separate the charges to infinity. This is analogous to a gravitational system where an object below the reference height has negative gravitational PE. The hydrogen atom, with an electron bound to a proton, is the classic example of a negative electric PE system.
What is the difference between potential energy and kinetic energy?
Potential energy is stored energy due to position or configuration — it is energy 'waiting to be released.' Kinetic energy is the energy of motion, given by KE = ½mv². In a conservative system (one with no friction or air resistance), total mechanical energy E = KE + PE remains constant. This is the law of conservation of energy. When a ball falls from a height, its gravitational PE decreases while its kinetic energy increases by the same amount. At the bottom of the fall, just before impact, all of the initial PE has converted to KE. Roller coasters, pendulums, and satellite orbits are all governed by this interplay. Springs and elastic bands store PE when deformed, releasing it as KE when they snap back.
How does the spring constant affect elastic potential energy?
The spring constant k (also called the stiffness coefficient) measures how resistant a spring is to deformation. A higher k means a stiffer spring that requires more force to compress or extend by the same distance. Because elastic PE = ½kx², a stiffer spring stores more energy for the same displacement. For example, a car suspension spring with k = 25,000 N/m compressed by 10 cm (0.1 m) stores PE = ½ × 25,000 × 0.01 = 125 J. A soft bungee cord with k = 60 N/m stretched by 10 m stores PE = ½ × 60 × 100 = 3,000 J — much more energy due to the large displacement, despite a much lower spring constant.
Why does gravitational acceleration differ on other planets?
Gravitational acceleration at a planet's surface is determined by g = GM/R², where G is the universal gravitational constant, M is the planet's mass, and R is its radius. Larger planets have stronger gravity not simply because they are bigger, but because of the ratio of mass to radius squared. Jupiter, with a mass 318 times Earth's but a radius only 11 times larger, has a surface gravity of about 24.79 m/s² — roughly 2.5 times Earth's. The Moon, being both much less massive and much smaller than Earth, has g = 1.62 m/s², about one-sixth of Earth's gravity. This means the same object at the same height stores about six times less gravitational PE on the Moon than on Earth.
How do I convert joules to kilocalories (food calories)?
One food calorie (kcal, the 'Calorie' on nutrition labels) equals exactly 4,184 joules. To convert a potential energy result from joules to kilocalories, divide by 4,184. For example, a 70 kg person climbing a 3-meter ladder stores approximately 2,060 J of gravitational PE, which equals 2,060 / 4,184 ≈ 0.49 kcal — less than half a food calorie. This illustrates why physical activity burns only small amounts of the stored food energy: most of the metabolic energy goes into heat, and the actual mechanical work performed is a small fraction. Our calculator automatically shows the kcal conversion alongside all other energy units in the conversions table.