Energy⏱ 4 min read

Gravitational Potential Energy

PE = mgh

What is the Gravitational Potential Energy?

Gravitational potential energy is the energy stored in an object because of its height above a reference point, usually the ground. Lift an object higher and it gains more potential energy — energy that converts back into kinetic energy as the object falls.

The reference point (h = 0) is a choice, not a fixed rule — potential energy is always relative to wherever you decide to measure height from, which is why only changes in PE, not its absolute value, usually matter in physics problems.

What Each Variable Means

Potential energyThe stored energy due to position. (joules (J))

MassThe mass of the object. (kilograms (kg))

Gravitational accelerationOn Earth, g ≈ 9.81 m/s² (often rounded to 10 m/s² for quick estimates). (m/s²)

HeightThe vertical height above the chosen reference point. (meters (m))

When to Use It

Calculating the stored energy of a raised object
Analyzing energy conversion between potential and kinetic energy, like a falling or swinging object
Estimating the energy released when something falls a known height

Step-by-Step Examples

Example 1: Calculating potential energy

Problem: A 5 kg book is lifted to a shelf 2 m above the floor. What is its potential energy?

Identify the known values

Mass, gravitational acceleration, and height.

m = 5 kg, g = 9.81 m/s², h = 2 m

Apply the formula

Multiply all three together.

PE = 5 × 9.81 × 2

✓

Answer: PE = 98.1 J

Example 2: Energy converted as an object falls

Problem: A 2 kg rock falls from a height of 10 m. How much potential energy converts to kinetic energy by the time it hits the ground?

Calculate the initial potential energy

All of it converts to kinetic energy by the time the rock reaches h = 0.

PE = m × g × h = 2 × 9.81 × 10

✓

Answer: PE = 196.2 J, all of which becomes kinetic energy at impact

Interactive Calculator

m (mass) (kg)g (gravity) (m/s²)h (height) (m)

Result will appear here

Common Mistakes

Mistake: Using an inconsistent value of g without noting it.
Fix: g ≈ 9.81 m/s² is standard; 10 m/s² is a common rounded approximation. Either is fine for most problems, but be consistent and note which one you're using.
Mistake: Measuring height from the wrong reference point.
Fix: Height must be measured from whatever point you're treating as PE = 0 — usually the ground or the lowest point in the problem, not an arbitrary starting height.

Practice Questions

A 10 kg object sits 4 m above the ground. Find its potential energy (use g = 9.81 m/s²).
What height gives a 2 kg object 100 J of potential energy?
Hint: Rearrange PE = mgh to solve for h.

Frequently Asked Questions

Why does the choice of reference point not matter for physics problems?

Because what usually matters is the change in potential energy (as an object rises or falls), not its absolute value — shifting the reference point up or down shifts every PE value by the same constant, leaving differences unchanged.

What happens to potential energy as an object falls?

It converts into kinetic energy — in the absence of air resistance, the potential energy lost exactly equals the kinetic energy gained, by conservation of energy.