Potential Energy Calculator – PE = mgh
Calculate gravitational potential energy from mass, height, and gravitational acceleration. Enter the values in kg, m, and m/s² to get the result in joules instantly.
Calculate Potential Energy
Potential Energy Formula
Where:
- \(PE\) — potential energy (joules, J)
- \(m\) — mass of the object (kg)
- \(g\) — gravitational acceleration (m/s², about 9.8 on Earth)
- \(h\) — height above the reference level (m)
The formula expresses the energy an object stores simply because it sits at a height \(h\) above a chosen reference level in a gravitational field. That energy equals the work needed to lift the object to that height, and it is released as kinetic energy when the object falls.
Potential Energy – Calculation Example
Example: a 10 kg crate is lifted onto a shelf 5 m above the floor. Using the default gravitational acceleration of 9.8 m/s²:
\[ PE = m \cdot g \cdot h = 10 \times 9.8 \times 5 = 490 \text{ J} \]
Result: the crate stores 490 J of gravitational potential energy.
How to Use the Potential Energy Calculator
- Enter the object's Mass in kilograms (kg).
- Enter the Height of the object above your reference level (usually the ground) in meters (m).
- Enter the Acceleration of Gravity in m/s². The default is 9.8 for Earth's surface; change it for other planets or altitudes.
- Read the Potential Energy result, displayed in joules (J).
What Is Potential Energy?
Potential energy is the energy an object has because of its position or configuration rather than its motion. Gravitational potential energy — the type this calculator computes — comes from an object's height within a gravitational field. A book on a shelf, water behind a dam, and a lifted crane load all carry potential energy that can be converted into other forms, most commonly kinetic energy, when they are released.
The value of \(PE\) depends on the choice of a reference level (where \(h = 0\)). Usually the ground or the floor is the natural choice, so the calculated energy tells you how much work gravity can do if the object falls back to that level. Physically, only changes in potential energy matter: raising the crate in the example from 0 m to 5 m required 490 J of work against gravity, and that same 490 J can be recovered during the descent.
Interpreting the result is straightforward: a larger mass or a greater height means proportionally more stored energy. Doubling the height doubles the potential energy, and so does doubling the mass. If the object falls freely, all of this energy converts into kinetic energy just before impact (neglecting air resistance) — you can explore that conversion with our Free Fall Calculator or see how gravity drives the motion with the Projectile Motion Calculator.
Assumptions, Limitations, and Tips
- Uniform gravity: the formula assumes \(g\) is constant over the height involved. This is excellent near Earth's surface but breaks down for satellites or very tall structures.
- Reference level: the result is measured relative to wherever you set \(h = 0\). Be consistent when comparing energies — always measure heights from the same level.
- Gravitational acceleration varies: use 9.8 m/s² for Earth, 1.62 for the Moon, or 3.71 for Mars. The Weight on Planets Calculator shows how \(g\) differs across the solar system.
- Only gravitational energy: this tool does not cover elastic potential energy (for springs, see the Hooke's Law Calculator) or other forms such as chemical or electrical potential energy.
- No friction or losses: the calculation is idealized; real lifting systems lose energy to friction, so actual work input is higher than the computed \(PE\).
Typical Values of Gravitational Acceleration
| Location | \(g\) (m/s²) |
|---|---|
| Earth (average surface) | 9.8 |
| Moon | 1.62 |
| Mars | 3.71 |
| Jupiter | 24.79 |
| Space station orbit (microgravity) | ≈ 0 (effective) |
Simply enter the appropriate value in the Acceleration of Gravity field to compute potential energy on another world.
Frequently Asked Questions
How do I calculate potential energy without a calculator?
Multiply mass by gravity by height: \(PE = m \cdot g \cdot h\). For quick mental math on Earth, round gravity to 10 m/s², so a 60 kg person on a 3 m ledge stores about \(60 \times 10 \times 3 = 1800\) J. For a precise hand calculation use \(g = 9.8\) m/s², multiply the three numbers, and express the answer in joules.
What is a good or normal value for potential energy?
There is no universal "normal" value — it depends entirely on mass and height. A 1 kg book on a 1 m shelf holds 9.8 J; a 1500 kg car raised on a 2 m lift holds 29,400 J. Useful benchmarks: 1 J lifts an apple (about 100 g) one meter, and food energy is often quoted in kilojoules (1 kJ = 1000 J) or Calories (1 Cal ≈ 4184 J).
How do I convert the result from joules to other units?
1 kilojoule (kJ) = 1000 J, 1 megajoule (MJ) = 1,000,000 J. In imperial units, 1 joule ≈ 0.7376 foot-pounds (ft·lb). If you prefer to work in pounds and feet, note that weight in pounds already includes gravity, so potential energy equals weight × height directly in ft·lb — a 100 lb object at 10 ft stores 1000 ft·lb.
What happens if the height is negative or zero?
A negative height is physically fine: it simply means the object sits below your chosen reference level, so its potential energy is negative. A zero height gives zero energy. Since only differences in potential energy matter, negative values are meaningful — for example, water at the bottom of a valley relative to a hilltop has negative PE that becomes available when pumped up.
Why does the reference level matter, and how do I choose it?
The formula measures height above a level you pick as zero, so the same object can have different PE values depending on that choice. Pick whichever level is most convenient for the problem — the ground, the floor, or a tabletop — but use the same one throughout your analysis. Only changes in PE have physical meaning, so any consistent choice gives correct results.
Can this formula be used for satellites or very high altitudes?
No. The formula \(PE = mgh\) assumes gravity is constant, which holds well only near a planet's surface. For satellites or altitudes of hundreds of kilometers, gravity weakens with distance, and you must use the general formula \(PE = -G \frac{m_1 m_2}{r}\), where \(G\) is the gravitational constant and \(r\) the distance between the centers of the two bodies.
What are common mistakes when calculating potential energy?
The most frequent errors are mixing units (pounds with meters, or grams instead of kilograms), measuring height from inconsistent reference levels, and forgetting that mass must be in kg. Another pitfall is confusing gravitational PE with elastic PE in springs — they use different formulas. Also remember the result is ideal: real lifting systems lose energy to friction, so the actual work needed is slightly higher than the calculated value.