Classical Mechanics

Gravitational PE Calculator

Solve PE = mgh for potential energy, mass, height or gravity. Works for any planet.

Gravity (g) — m/s²

Mass (m) — kg

Height (h) — m

Result

PE = mgh

Step-by-Step Solution

What is Gravitational Potential Energy?

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. The higher an object is raised above a reference point, the more GPE it stores. When released, this energy converts to kinetic energy — the principle behind roller coasters, hydroelectric dams, and falling objects.

PE = mgh

m = mass (kg) | g = gravitational acceleration (m/s²) | h = height above reference (m)

Variables Explained

Symbol	Name	Unit	Description
PE	Potential Energy	J	Energy stored due to position in a gravity field
m	Mass	kg	Amount of matter in the object
g	Gravity	m/s²	9.81 m/s² on Earth; 1.62 on Moon; 3.72 on Mars
h	Height	m	Vertical distance above the chosen reference point

💡 GPE is measured relative to a chosen reference level. Only changes in GPE are physically meaningful. The ground, sea level, or any convenient point can be h = 0.

Conservation of Energy

In a frictionless system, mechanical energy is conserved: PE + KE = constant. As an object falls from height h, its PE decreases while its KE increases by exactly the same amount. At the lowest point, all PE has converted to KE. This is why a ball dropped from 5 m always reaches the same speed at the bottom, regardless of how it was released.

Real-World Applications

⛰️

Hydroelectric Power

Water stored at height has GPE that converts to electrical energy as it falls through turbines.

🎢

Roller Coasters

At the top of a hill, kinetic energy is stored as GPE. The descent converts it back to speed.

🔋

Pumped Storage

Excess electricity pumps water uphill (storing GPE) to release during peak demand.

🏋️

Weight Training

Lifting a barbell converts muscle energy into GPE stored in the weight.

Frequently Asked Questions

What is the reference point for GPE?

Any height can be chosen as the reference (h = 0). What matters is the change in height. In problems, the ground is usually chosen as reference. The absolute value of GPE is meaningless; only differences matter.

How is GPE related to kinetic energy?

By conservation of energy: PE + KE = constant (in frictionless systems). When an object falls, it loses PE and gains exactly the same amount of KE. At the bottom, all PE is converted to KE.

Does GPE depend on the path taken?

No. GPE depends only on the height difference, not on the path. This makes gravity a conservative force. Climbing a ramp or a ladder to the same height requires the same change in GPE.