Potential Energy Calculator
This potential energy calculator helps you instantly compute the gravitational potential energy stored in an object based on its mass, height above a reference point, and the local gravitational acceleration. It supports both the metric (SI) and imperial (US customary) unit systems and displays results in multiple energy units — joules, kilojoules, kilocalories, watt-hours, BTU, and foot-pounds.
How to Calculate Potential Energy
Gravitational potential energy (PE) is the energy an object possesses due to its position in a gravitational field. The higher an object is raised, and the heavier it is, the more energy it stores — energy that can be released as the object falls or moves to a lower position.
To calculate potential energy you need three values:
- Mass (m) — the mass of the object (kg or lb).
- Height (h) — the vertical height above the reference level (m or ft).
- Gravitational acceleration (g) — on Earth's surface: 9.81 m/s² (metric) or 32.174 ft/s² (imperial). You can enter a custom value for other planets or environments.
The Potential Energy Formula
The gravitational potential energy formula is:
PE = m × g × h
Where:
- PE — gravitational potential energy (J in metric; ft·lbf in imperial).
- m — mass of the object.
- g — gravitational acceleration (default 9.81 m/s² on Earth).
- h — height above the reference level.
For the imperial system, the formula accounts for the gravitational constant gc = 32.174 lbm·ft/(lbf·s²):
PE (ft·lbf) = m (lb) × g (ft/s²) × h (ft) / 32.174
At standard gravity (g = 32.174 ft/s²), this simplifies to PE = m × h, meaning the foot-pounds value equals mass (lb) × height (ft).
Practical Examples
Example 1: Apple on a Tree (Metric)
An apple with mass 0.1 kg hangs at a height of 2.5 m:
PE = 0.1 kg × 9.81 m/s² × 2.5 m = 2.4525 J
Example 2: Wrecking Ball (Metric)
A wrecking ball with mass 1,000 kg raised to 10 m:
PE = 1,000 kg × 9.81 m/s² × 10 m = 98,100 J = 98.1 kJ
Example 3: Rock on a Cliff (Imperial)
A rock weighing 50 lb on a cliff 30 ft high:
PE = 50 lb × 30 ft = 1,500 ft·lbf (at standard gravity)
Energy Unit Conversions
| Unit | Equivalent in Joules |
|---|---|
| 1 Joule (J) | 1 J |
| 1 Kilojoule (kJ) | 1,000 J |
| 1 Kilocalorie (kcal) | 4,184 J |
| 1 Watt-hour (Wh) | 3,600 J |
| 1 BTU | 1,055.06 J |
| 1 Foot-pound (ft·lbf) | 1.35582 J |
Frequently Asked Questions
What is potential energy?
Potential energy is stored energy resulting from an object's position or state. Gravitational potential energy is the most common type — it is the energy stored by an object due to its height above a reference point. When released, it converts into kinetic energy (the energy of motion).
What is the gravitational acceleration on Earth?
On Earth's surface the standard gravitational acceleration is g = 9.80665 m/s², commonly rounded to 9.81 m/s² (or 1 g). In imperial units this equals 32.174 ft/s². The calculator uses 9.81 m/s² by default; you can override this for other planets or altitudes.
What happens when height is zero?
If the height is zero, the potential energy is also zero. An object resting on the reference level (e.g., the ground) has no gravitational potential energy relative to that level.
How does doubling mass or height affect PE?
The relationship is linear: doubling the mass or the height doubles the potential energy. Doubling both quadruples it.
How is potential energy related to kinetic energy?
When an object falls freely (ignoring air resistance), all of its potential energy converts to kinetic energy (KE = ½mv²). At any intermediate height, the total mechanical energy (PE + KE) remains constant — this is the law of conservation of energy.
What is the difference between metric and imperial PE?
In the metric (SI) system, potential energy is measured in Joules (J): PE = m(kg) × g(m/s²) × h(m).
In the US customary (imperial) system, it is measured in foot-pounds force (ft·lbf): PE = m(lbm) × h(ft) at standard gravity. The calculator handles the gravitational constant conversion automatically.