Free Potential Energy Calculator
Calculate gravitational potential energy with the formula PE = m·g·h. Enter an object's mass, its height above a reference point, and the acceleration due to gravity to get the stored energy in joules and kilojoules instantly.
Enter mass and height to calculate gravitational potential energy (PE = m·g·h).
Uses standard gravity g = 9.80665 m/s² by default. Set g = 1.62 for the Moon or 3.72 for Mars. Height is measured from your chosen reference level (PE = 0).
Quick answer
Gravitational potential energy is calculated with PE = m·g·h, where m is mass in kilograms, g is the acceleration due to gravity (9.80665 m/s² on Earth), and h is the height in meters above a chosen reference level. The result is in joules (J). For example, a 2 kg object raised 10 m has PE = 2 × 9.80665 × 10 = 196.13 J.
Formula & method
PE = m · g · h
- PE — Gravitational potential energy (joules, J)
- m — Mass of the object (kilograms, kg)
- g — Acceleration due to gravity (m/s²); 9.80665 on Earth
- h — Height above the reference level (meters, m)
Gravitational potential energy in joules (J). Multiply mass (kg) by gravitational acceleration (m/s²) by height (m). On Earth, g = 9.80665 m/s² (standard gravity).
1 kJ = 1000 J
Convert joules to kilojoules by dividing by 1000. Useful when the energy value becomes large, such as for heavy masses or great heights.
Examples
- Input
- m = 2 kg, h = 10 m, g = 9.80665 m/s²
- Result
- 196.13 J
- Why
- PE = m·g·h = 2 × 9.80665 × 10 = 196.133 J ≈ 196.13 J. This is the energy stored when a 2 kg object is raised 10 m on Earth.
- Input
- m = 1.5 kg, h = 2 m, g = 9.80665 m/s²
- Result
- 29.42 J
- Why
- PE = 1.5 × 9.80665 × 2 = 29.41995 J ≈ 29.42 J. A 1.5 kg book sitting on a 2 m shelf has about 29.4 joules of gravitational potential energy relative to the floor.
- Input
- m = 5000 kg, h = 120 m, g = 9.80665 m/s²
- Result
- 5,883,990 J (5,883.99 kJ)
- Why
- PE = 5000 × 9.80665 × 120 = 5,883,990 J = 5,883.99 kJ. Five tonnes of water behind a 120 m dam stores nearly 5.9 megajoules, which can be released to drive a turbine.
- Input
- m = 10 kg, h = 3 m, g = 1.62 m/s²
- Result
- 48.60 J
- Why
- PE = 10 × 1.62 × 3 = 48.6 J. Using the Moon's surface gravity of 1.62 m/s² instead of Earth's 9.80665 m/s² gives a much smaller potential energy for the same lift height.
When to use this tool
- Solving physics homework or exam problems involving gravitational potential energy and the conservation of energy.
- Estimating the energy stored in a raised object, a water reservoir, or a pumped-storage system before it is released.
- Checking energy conversions, such as how much kinetic energy an object will have at the bottom of a fall (ignoring air resistance).
- Comparing potential energy on different bodies (Earth, Moon, Mars) by changing the gravitational acceleration g.
Common mistakes
- Using grams instead of kilograms for mass. The joule formula requires SI units, so convert grams to kilograms (divide by 1000) before calculating.
- Measuring height in centimeters or feet. Height must be in meters; convert first (1 ft = 0.3048 m, 1 cm = 0.01 m) or the answer will be off by a large factor.
- Forgetting that potential energy is relative to a reference level. PE depends on the height h above whatever point you call 'zero'; choosing a different reference changes the value.
- Using g = 9.81 or g = 10 when high precision is needed. Standard gravity is 9.80665 m/s²; rounding g introduces small errors that matter in engineering and exam work.
Frequently asked questions
What is the formula for gravitational potential energy?
The formula is PE = m·g·h, where m is mass in kilograms, g is the acceleration due to gravity (9.80665 m/s² on Earth), and h is the height in meters above your reference level. The result is in joules (J).
What value of g should I use?
For Earth, use the standard gravity g = 9.80665 m/s², which this calculator uses by default. Many textbooks round to 9.81 or even 9.8 m/s². For other bodies, use 1.62 m/s² for the Moon and 3.72 m/s² for Mars.
What units does this calculator use?
It uses SI units: mass in kilograms (kg), height in meters (m), and gravity in m/s². The output is in joules (J) and kilojoules (kJ). Convert any imperial inputs to SI units first for a correct answer.
Why does potential energy depend on a reference level?
Only differences in potential energy are physically meaningful, so you must pick a height where PE = 0 (often the ground or floor). The h in PE = m·g·h is the height above that chosen reference, so a different reference gives a different numerical value.
How is potential energy related to kinetic energy?
In the absence of friction or air resistance, gravitational potential energy converts to kinetic energy as an object falls. At the moment of release the energy is all PE; just before impact it is all KE, so m·g·h = ½·m·v². This lets you find impact speed from the drop height.
Can I calculate potential energy in calories or other units?
This tool reports joules and kilojoules, the SI energy units. To convert, divide joules by 4.184 to get calories, or by 4184 to get kilocalories (dietary Calories). 1 kWh equals 3,600,000 J.
Sources & references
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