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Potential Energy Calculator

Physics

Calculate gravitational potential energy using PE = mgh. Enter mass, height, and gravity to get stored energy in joules instantly, with an editable gravity field.

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Potential Energy

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This calculator computes your Potential Energy from the values you enter.

Inputs
MassHeightGravitational Acceleration
Outputs
Potential Energy

What is a Potential Energy?

The Potential Energy Calculator computes gravitational potential energy using PE = m × g × h — the energy an object has stored due to its height above a reference point. Enter a mass, a height, and a gravitational acceleration value (defaulting to Earth's 9.8 m/s², but editable for other planets or scenarios), and the calculator instantly returns the potential energy in joules.

Gravitational potential energy is one of the foundational concepts in mechanics, directly connected to work, kinetic energy, and the principle of energy conservation. This calculator makes it easy to explore how potential energy scales with mass, height, and gravitational strength.

If you want to know what happens as that potential energy converts to motion, use the Free Fall Calculator to find the resulting velocity, or the Kinetic Energy Calculator to verify energy conservation.

How to use this Potential Energy calculator

  1. Enter the mass — the mass of the object in kilograms.

  2. Enter the height — the vertical height above your reference point, in meters.

  3. Set the gravity value — defaults to 9.8 m/s² for Earth; change it to model other planets or precise local gravity.

  4. Read the potential energy result — the highlighted result shows the stored gravitational potential energy in joules.

  5. Check the step-by-step breakdown — expand the calculation steps to see the exact formula substitution, and compare with the Kinetic Energy Calculator to verify energy conservation as the object falls.

Formula & Methodology

Gravitational potential energy formula:
PE = m × g × h

Variable definitions:
- m — mass (kilograms)
- g — gravitational acceleration (meters per second squared, 9.8 on Earth by default)
- h — height above the reference point (meters)
- PE — potential energy (joules)

Worked example:

A 20 kg object is lifted 5 meters on Earth (g = 9.8 m/s²).

Step 1 — Apply the formula: PE = 20 kg × 9.8 m/s² × 5 m = 980 J

This means 980 joules of energy are stored in the object due to its elevated position — energy that converts almost entirely into kinetic energy if the object is dropped, verifiable using the Free Fall Calculator and Kinetic Energy Calculator.

Note: This calculator computes gravitational potential energy only. Other forms of potential energy (elastic, electrical, chemical) use different formulas not covered by this tool.

Frequently Asked Questions

Gravitational potential energy is calculated as PE = m × g × h, where m is mass in kilograms, g is gravitational acceleration in meters per second squared, and h is height in meters above a reference point. The result is expressed in joules (J). This calculator applies that formula directly to whatever values you enter.
Gravitational acceleration varies by location — it's about 9.8 m/s² on Earth, but roughly 1.62 m/s² on the Moon and 3.7 m/s² on Mars. Making gravity an editable input lets you calculate potential energy for any celestial body or hypothetical scenario, not just Earth.
The default is 9.8 m/s², the standard approximation for Earth's gravitational acceleration at sea level. You can change this value to model potential energy on other planets or in scenarios requiring a more precise local gravity value (which varies slightly with latitude and altitude).
Yes — if height is measured relative to a reference point above the object (rather than below it), the object's potential energy relative to that point is negative. This calculator assumes height is measured upward from your chosen reference level, so a positive height gives positive potential energy.
As an object falls, its potential energy converts into kinetic energy, and in the absence of air resistance, the total mechanical energy (potential + kinetic) stays constant. Use the [Kinetic Energy Calculator](/kinetic-energy-calculator/) to see how much kinetic energy an object gains as it falls a given height, which should match the potential energy lost.
A 5 kg object held 2 meters above the ground has a potential energy of about 98 J (5 × 9.8 × 2), which converts almost entirely into kinetic energy by the time it hits the ground (ignoring air resistance) — a value you can verify with the [Free Fall Calculator](/free-fall-calculator/) and [Kinetic Energy Calculator](/kinetic-energy-calculator/).
Rearrange the formula to solve for height: h = PE ÷ (m × g). Divide your target potential energy by the product of mass and gravity to find the required height. This calculator computes PE forward from height, mass, and gravity, but the same formula works in reverse with simple algebra.
No — this calculator computes gravitational potential energy only (PE = mgh). Other forms, like elastic potential energy in a spring (PE = ½kx²) or electrical potential energy, use different formulas and are not covered by this tool.
Gravitational potential energy calculations are fundamental to hydroelectric power generation (water stored at height converts to kinetic energy and then electricity), pumped-storage energy systems, elevator and crane design, and structural engineering for anything involving elevated mass.
The work done against gravity to lift an object to a given height equals the potential energy gained — they're numerically identical (W = PE = mgh). Use the [Work Calculator](/work-calculator/) to compute work done by any force, including the special case of lifting against gravity.
Potential energy (PE = mgh) is linear in both mass and height because it's derived from a constant gravitational force acting over a distance — unlike kinetic energy, which involves velocity squared because of how energy relates to acceleration over distance. Doubling either mass or height simply doubles potential energy.
Yes — as long as you use the vertical height gained (not the distance traveled along the incline), the formula PE = mgh still applies correctly, since gravitational potential energy depends only on vertical height, not the path taken to get there.
Also known as
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