Potential Energy
Solve PE = mgh for gravitational potential energy, mass, or height. Free calculator with g choices, unit-aware inputs, and step-by-step working.
Key formula
PE = mgh
How do you calculate potential energy (PE = mgh)?
Near Earth’s surface, PE = m g h. Multiply mass (kg) by g (usually 9.8 m/s²) by height (m) above your chosen zero. The result is in joules. Rearrange to m = PE/(g h) or h = PE/(m g) when energy is given.
About this tool
Gravitational potential energy stores how high a mass sits in a gravitational field. This tool keeps the mgh formula PE = m g h visible so you can solve for energy, mass, or height without losing the reference-level and unit checks that usually cost marks.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: how to calculate PE for 2.0 kg lifted 1.5 m
A 2.0 kg box is lifted 1.5 m with 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 — always use the paper’s g.
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 without converting wrongly gives ~941 J.
Frequently asked questions
What is the formula for gravitational potential energy?
Near Earth’s surface, PE = m g h (the mgh formula), where m is mass, g is gravitational field strength, and h is height above a chosen reference. Rearrangements are m = PE / (g h) and h = PE / (m g).
How do you calculate potential energy step by step?
Choose PE = 0, convert mass to kg and height to m, pick the paper’s g, then multiply PE = m g h. Check that a few kilograms lifted about a metre store tens of joules, not thousands.
What does mgh mean in physics?
mgh is the product of mass, gravitational field strength, and height. It estimates gravitational potential energy in the near-surface model used in most school problems.
Should I use g = 9.8 or g = 10?
Use the value given on the exam or worksheet. Many courses accept 9.8 m/s² or 10 m/s² for estimates; some want 9.81. Do not mix two different g values in one answer.
From where do I measure height h?
From whatever level you define as PE = 0 — floor, table, or ground — as long as you stay consistent. Energy differences between two heights depend on Δh.