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What does this calculator estimate?
A 5 kg object 10 meters up has about 490.5 joules of gravitational potential energy: PE = 5 x 10 x 9.81 = 490.5 J. Potential energy equals mass x height x gravity.
- Gravitational PE (J) = mass (kg) x height (m) x gravity (9.81 m/s^2).
- Potential energy converts to kinetic energy as the object falls.
- The joule is the SI unit of energy (NIST).
What potential energy is
Potential energy is stored energy due to position — a lifted object can do work when it falls. Gravitational PE = mgh assumes the height is small compared to Earth's radius, so gravity stays constant.
Limitations to watch for
The formula uses the height above the chosen reference level — changing the reference changes the number. Near Earth's surface g ≈ 9.81; on the Moon it's 1.62. For very large heights, use the full gravitational formula.
How to use it in practice
Choose a reference height (usually the ground), measure the mass and height, and compute. Combine with kinetic energy to analyze falling objects and pendulums via conservation of energy.
['Enter the mass in kilograms.', 'Enter the height in meters.', 'Optionally adjust gravity; the tool computes PE = mgh.']
What potential energy is
Gravitational potential energy is the energy stored by height: PE = m × g × h. A 10 kg object at 5 meters has 10 × 9.81 × 5 ≈ 490.5 joules. The calculator applies the standard gravity value.
The g value
Standard gravity is 9.81 m/s² on Earth's surface; the calculator uses it by default and lets you change it for other contexts. In imperial units, the equivalent formula uses weight and height in feet with a conversion factor.
Where potential energy shows up
Potential energy converts to kinetic energy when an object falls: the speed at impact follows from energy conservation. It also powers hydroelectric dams and pendulum clocks — the stored-height energy is the same principle.
A worked example
A 2 kg book on a 1.5 m shelf holds 2 × 9.81 × 1.5 ≈ 29.4 J. Dropped, it reaches about 5.4 m/s at the floor. The calculator returns the energy; the velocity follows from energy conservation.
Units and conversions
Energy comes out in joules (J); 1 J = 1 kg·m²/s². Common conversions: 1 kcal ≈ 4,184 J; 1 kWh = 3.6 MJ. The calculator works in SI units, the standard for physics.
How this calculator works
Formula
Gravitational potential energy PE = m × g × h, where m is mass (kg), g is gravity (default 9.81 m/s² on Earth), and h is height (m). Units: joules.
Worked example
A 10 kg object lifted 2.0 m: PE = 10 × 9.81 × 2.0 = 196.2 J.
Assumptions to verify
- Gravity is constant (near Earth's surface).
- The reference height is defined by the user.
- The object is rigid and the motion is vertical.
Frequently asked questions
What is potential energy?
Stored energy from position — gravitational PE = mgh is the energy an object has because of its height.
How do I calculate it?
Multiply mass × gravity × height. 10 kg at 2 m: 10 × 9.81 × 2 = 196.2 J.
What is g?
Gravitational acceleration, 9.81 m/s² on Earth. The tool lets you change it for other bodies (Moon 1.62, Mars 3.71).
Why does the reference height matter?
PE is measured relative to a chosen zero level — the ground, a table, or sea level. Only differences matter for physics.
What happens when the object falls?
PE converts to kinetic energy: at impact, KE = mgh (ignoring air resistance). That's energy conservation.
Is this the only kind of potential energy?
No — elastic (springs: ½kx²), chemical, and electric potential energy exist. This tool handles gravitational.
Does this work at orbital heights?
Only approximately — above a few hundred km, gravity weakens and the full gravitational formula is needed.
What happens when it falls?
Potential energy converts to kinetic — the speed follows from conservation.
Cite this tool
BoringToolsKit. “Potential Energy Calculator.” boringtoolskit.com/potential-energy-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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