Potential Energy Formula (PE = mgh): Free Calculator & Examples
How to calculate potential energy with PE = mgh (the mgh formula). Worked examples plus a free potential energy calculator for mass, height, and joules.
How to Calculate Potential Energy (Quick Answer)
Near Earth’s surface, gravitational potential energy is PE = m g h (the mgh formula). Multiply mass in kilograms by g (usually 9.8 m/s²) by height in metres above your chosen zero. The answer is in joules (J).
Need a checked number now? Open the free potential energy calculator (PE = mgh) — then come back for reference-level traps and worked examples.
What Is the mgh Formula?
mgh means mass × gravitational field strength × height. It estimates gravitational potential energy (PE or Ug) in the near-surface model used in most school problems. The formula does not care how the object got there — only how high it is relative to a chosen PE = 0 level.
Lift a book onto a shelf and you do work against gravity; that work shows up as extra PE. Drop the book and stored PE converts into kinetic energy as it falls.
PE = mgh Rearrangements
Verify any rearrangement in the free PE calculator.
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.
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.
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.
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 Examples
Example 1: how to calculate PE for 2.0 kg lifted 1.5 m
Take g = 9.8 m/s² and the floor as PE = 0. PE = m g h = (2.0)(9.8)(1.5) = 29.4 J. Rough check with g = 10: about 30 J.
Example 2: mgh formula — find height from 25 J
A 0.50 kg ball stores 25 J relative to the ground. With g = 10 m/s², h = PE / (m g) = 25 / (0.50 × 10) = 5.0 m. With g = 9.8, h ≈ 5.1 m.
Example 3: pe = mgh with height in cm
m = 1.2 kg, h = 80 cm = 0.80 m, g = 9.8. PE = (1.2)(9.8)(0.80) = 9.408 J ≈ 9.41 J. Leaving h as 80 would wrongly give ~941 J.
Check Example 1–3 arithmetic on the potential energy calculator.
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.
Compare with how to calculate kinetic energy and the
Spring energy is different: elastic potential energy U = ½kx².
Common Mistakes
Free Potential Energy Calculator
Use the free potential energy calculator to solve PE = mgh for energy, mass, or height with unit-aware inputs and step-by-step working.
Work calculator — lifting against gravity is work that shows up as PE.
Weight calculator — W = mg before PE = W h.
Gravitational force calculator — when you leave the near-surface model.
Master PE = mgh with a clear zero height and consistent SI units — then verify every homework answer on the calculator.
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