How to Calculate Potential Energy (PE = mgh): Formula, Units & Worked Examples

Use PE = mgh with clear height references, g choices, and homework examples. Check every answer with a free potential energy calculator for mass, height, and joules.

What Gravitational Potential Energy Means

Gravitational potential energy (often written PE or Ug) is the energy an object stores because of its height in a gravitational field. Lift a book onto a shelf and you do work against gravity; that work shows up as extra PE. Drop the book and the stored energy converts into kinetic energy as it falls.

Near Earth’s surface, introductory problems use a simple model: PE = m g h. Mass m, gravitational field strength g, and height h above a chosen reference level. The formula does not care how the object got there — only how high it is relative to that zero point.

If you already have mass, height, and g and only need a checked number, open the free potential energy calculator first, then return here for reference-level traps and worked examples that usually cost marks.

The Formula PE = mgh and Rearrangements

Start from PE = m × g × h. Three rearrangements cover most homework:

m = PE / (g h) — find mass when energy and height are known.

h = PE / (m g) — find the height that stores a given energy.

g = PE / (m h) — less common, but useful when a problem asks you to back out g.

Isolate the unknown, substitute values with units, then multiply or divide. School SI defaults are kilograms, metres, and g ≈ 9.8 m/s² (or 9.81), so PE comes out in joules (J).

Choosing g: 9.8, 9.81, or 10

Use the value printed on the exam paper. Many courses accept g = 9.8 m/s² or g = 10 m/s² for estimates. Engineering-style problems often want 9.81. Mixing 9.8 in working and 10 in a “check” will make your answer look wrong even when the method is fine.

g is the gravitational field strength (N/kg), numerically equal to free-fall acceleration (m/s²) near Earth’s surface. On another planet, use that planet’s g — PE = mgh still applies in the same near-surface approximation.

Height and the Reference Point

Height h is measured from whatever level you call PE = 0. Floor, table, ground, or the bottom of a ramp can all be valid zeros if you stay consistent. Changing the zero shifts every PE value by the same amount; energy differences between two heights stay the same.

If a ball rises from 1.0 m to 3.0 m above the floor, the change in PE uses Δh = 2.0 m, not the absolute heights alone. Write the reference clearly before you substitute.

Unit Traps That Break Answers

Mass in grams

Convert grams to kilograms before multiplying (÷ 1000). Using 500 g as if it were 500 kg inflates PE by a factor of 1000.

Height in centimetres

Convert centimetres to metres (÷ 100) for SI joules. 80 cm is 0.80 m. Leaving height in cm while g is in m/s² produces a nonsense unit mix.

Weight vs mass

Weight is already a force (W = mg). Do not multiply weight by g again. If the problem gives weight in newtons, PE = W × h (same as mgh).

Worked Example 1: 2.0 kg Lifted 1.5 m

A 2.0 kg box is lifted vertically from the floor to a shelf 1.5 m high. Take g = 9.8 m/s² and the floor as PE = 0. Find the gravitational potential energy on the shelf.

PE = m g h = (2.0 kg)(9.8 m/s²)(1.5 m) = 29.4 J.

Sanity check: roughly 2 × 10 × 1.5 = 30 J. If you used g = 10, PE = 30 J — fine when the paper allows it.

Worked Example 2: Find Height from PE

A 0.50 kg ball stores 25 J of gravitational potential energy relative to the ground. With g = 10 m/s², how high is the ball?

Rearrange: h = PE / (m g) = 25 / (0.50 × 10) = 25 / 5.0 = 5.0 m above the chosen zero.

If the paper required g = 9.8, then h = 25 / (0.50 × 9.8) ≈ 5.1 m. Always match the g the question specifies.

Potential Energy vs Kinetic Energy

PE depends on height; kinetic energy depends on speed: KE = ½ m v². At the top of a throw, PE is high and KE is low; just before impact (ignoring air resistance), KE is high and PE is lower relative to the ground. Mechanical energy problems often track PE + KE when no non-conservative work is done.

To check motion energy after speed is known, use the kinetic energy calculator. For attraction between two masses far apart (not near-surface mgh), use Newton’s law on the gravitational force calculator instead.

Common Mistakes

Measuring h from the wrong reference or mixing two different zeros in one calculation.

Leaving mass in grams or height in centimetres while reporting joules.

Using weight in newtons as if it were mass in kilograms inside PE = mgh.

Forgetting that PE = mgh is a near-surface approximation — not the full 1/r gravitational potential for space problems.

Comparing PE numbers that used different g values without saying so.

Sanity check: lifting a few kilograms by about a metre stores tens of joules, not thousands, unless mass or height is huge.

Check Your Work with Free Calculators

Once the method is clear, verify the arithmetic. The potential energy calculator applies PE = mgh with unit-aware inputs so you can confirm mass, g, height, and the joule result.

Potential energy calculator — PE, mass, or height from mgh.

Kinetic energy calculator — when speed matters instead of height.

Gravitational force calculator — F = G m₁ m₂ / r² when you leave the near-surface model.

Work calculator — lifting against gravity is work that shows up as PE.

Master PE = mgh with a clear zero height and consistent SI units. That habit carries into energy conservation problems where PE trades with KE.

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