Potential Energy Calculator (PE = mgh)
Calculate gravitational potential energy PE = mgh. Enter mass, gravitational acceleration and height to get potential energy in Joules.
How to use this tool
- Enter mass, gravitational acceleration and height in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your potential energy and the full breakdown beneath it.
Gravitational potential energy is the energy stored by lifting an object: PE = mgh, where m is mass (kg), g is gravitational acceleration (9.81 m/s² on Earth), and h is height (m). On the Moon use g = 1.62 m/s².
Formula
PE = m × g × h
Where m = mass (kg), g = gravitational acceleration (m/s²), h = height (m). Result is in Joules (J).
How it works
This calculator computes gravitational potential energy — the energy stored in an object due to its position above a reference point. It multiplies mass, gravitational acceleration, and height directly. The formula assumes a uniform gravitational field, which is accurate near Earth's surface but becomes less precise at very large heights where gravity weakens.
Worked example
- Given: mass m = 10 kg, gravitational acceleration g = 9.81 m/s², height h = 5 m.
- Apply the formula: PE = m × g × h = 10 × 9.81 × 5.
- Calculate: 10 × 9.81 = 98.1, then 98.1 × 5 = 490.5 J.
Potential energy = 490.5 J
Common mistakes to avoid
- Using g = 9.8 m/s squared vs the standard 9.81 m/s squared without noting which standard the problem requires, causing small but marked discrepancies.
- Measuring height from an arbitrary datum instead of the reference point specified in the problem, leading to a sign or magnitude error.
- Entering mass in grams instead of kilograms, producing a result 1000x too large.
Key terms
- Gravitational potential energy
- Energy stored in an object because of its height above a reference level, equal to the work done against gravity to lift it there.
- Gravitational acceleration (g)
- The acceleration due to gravity acting on a free-falling object. At Earth's surface the standard value is 9.81 m/s².
- Reference height
- The baseline height (h = 0) from which potential energy is measured. Only differences in PE between two heights are physically meaningful.
- Joule (J)
- The SI unit of energy. 1 J = 1 kg·m²/s², equal to the work done by a 1 N force over 1 metre.
Frequently asked questions
- What is the reference height?
- PE is always relative to a chosen reference (usually the ground). Only differences in PE matter for energy calculations.
- How is PE related to KE?
- In a frictionless fall, PE converts entirely to KE: mgh = ½mv², giving v = √(2gh) at impact.