Potential Energy Calculator - PE = mgh

Mass

01,000,000

Height

0100,000

Gravitational Acceleration

0.130

Potential Energy

1,470

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.

Why Use a Potential Energy Calculator?

PE = mgh is a straightforward multiplication, but a dedicated calculator saves time when comparing multiple scenarios, different heights, masses, or even different planets' gravity, without manual recalculation each time.

The result updates live as you adjust any of the three inputs, and the step-by-step breakdown shows exactly how the formula was applied, making it easy to verify your work or explore "what if" questions about height, mass, or location.

Because gravity is editable, this calculator doubles as a tool for exploring physics beyond Earth, useful for space science education or mission planning estimates.

Who Should Use This Calculator?

Physics students verifying homework problems involving gravitational potential energy and energy conservation.

Engineers working on hydroelectric, pumped-storage, elevator, or crane systems where elevated mass and stored energy are central design considerations.

Teachers demonstrating how potential energy scales with height, mass, and gravitational strength, including comparisons across different planets.

Space science enthusiasts and students exploring how potential energy calculations change on the Moon, Mars, or other celestial bodies by adjusting the gravity input.

Hobbyists and makers estimating the stored energy in elevated objects for projects involving lifting mechanisms or falling-object experiments.

What Insights Does This Calculator Give You?

Potential Energy, the single result of the formula, expressed in joules (J), representing the gravitational potential energy stored in the object at the given height.

Linear scaling, unlike kinetic energy, potential energy scales linearly with both mass and height, so doubling either one exactly doubles the result. This calculator makes that direct proportionality easy to verify.

Cross-planet comparison, by adjusting the gravity input, you can see how the same mass and height produce very different potential energy values on Earth versus the Moon or Mars, useful for space science contexts.

How to use this Potential Energy calculator

Enter the mass, the mass of the object in kilograms.
Enter the height, the vertical height above your reference point, in meters.
Set the gravity value, defaults to 9.8 m/s² for Earth; change it to model other planets or precise local gravity.
Read the potential energy result, the highlighted result shows the stored gravitational potential energy in joules.
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.

Show formula & methodology ↓Show less ↑

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

What is the formula for gravitational potential energy?

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.

Why does this calculator let me change the gravity value?

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.

What is the default gravity value used here?

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).

Can potential energy be negative?

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.

How is potential energy related to kinetic 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.

What is a typical potential energy value in everyday terms?

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/).

How do I find the height an object needs to reach a target potential energy?

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.

Does this calculator account for elastic or other forms of potential energy?

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.

How is potential energy used in engineering and energy systems?

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.

What is the relationship between potential energy and work?

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.

Why does mass have a linear effect on potential energy while other physics formulas involve squares?

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.

Can I use this calculator for objects on inclined surfaces?

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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