Gravitational Potential Energy Calculator
PEg = mgh
Answer
Gravitational potential energy problems look easy on paper—until you are converting a textbook height in feet to meters, debating whether to use 9.81 or 9.80665 for gravity, and trying to express the answer in joules when your mass came in pounds. I have seen lab groups redo entire worksheets because one person used the floor as zero height while another used the table surface. This calculator keeps the algebra and unit conversions in one place so you can focus on the physics.
How to Use This Gravitational Potential Energy Calculator
- Choose what to solve for. Use the dropdown to calculate potential energy PEg, mass m, gravity g, or height h. The output field locks and shows (calculated) while you enter the other three values.
- Enter your known values. Pick energy, mass, gravity, and height units from each row’s dropdown—mixed units on one run are fine. Gravity defaults to 9.81 m/s² for typical Earth problems.
- Set significant figures. Leave auto or choose 3–9 sig figs to match your assignment.
- Press Calculate. The missing variable appears in the answer panel and in the calculated field, with the rearranged formula shown below.
To get started on a standard problem: leave the mode on Calculate PE | Given m, g, and h, enter mass and height from the diagram, confirm gravity (usually 9.81 m/s² on Earth), and read joules in the answer. If the question gives energy and asks for height—common on roller-coaster tracks—switch to Calculate h | Given PE, m, and g instead of rearranging the formula on paper.
Gravitational Potential Energy Formulas and Practical Applications
Think of a book resting on a high shelf: it is not moving, but it could do work if it fell. That stored “could fall” energy is gravitational potential energy—tied to how heavy the object is, how strong gravity is, and how far above your reference level it sits.
PEg = mgh
PEg is energy (joules by default), m is mass, g is gravitational acceleration, and h is vertical height above the reference you choose—usually the ground or lab floor.
Classic example: m = 3 kg, g = 9.81 m/s², h = 5 m gives PEg = 147.15 J. Need mass instead? m = PEg / (gh). Need height? h = PEg / (mg). Need gravity on another planet? g = PEg / (mh).
Where this shows up in real work
- Intro physics and AP problems: energy at the top of a ramp, cliff, or roller-coaster hill.
- Comparing stored energy before and after lifting a load with a hoist or crane (rough estimates).
- Planet or moon scenarios—swap g for lunar or Martian gravity from the table below.
- Conservation-of-energy setups where GPE at the top converts to kinetic energy at the bottom.
In a frictionless drop problem, PEg at height h becomes kinetic energy at ground level. Run the numbers here first, then check resulting speed with the Kinetic Energy Calculator if the assignment asks for velocity.
Standard Units
Potential energy units
| Unit | Symbol | Notes |
|---|---|---|
| Joule | J | SI default; 1 J = 1 N·m |
| Kilojoule | kJ | 1 kJ = 1,000 J |
| Megajoule | MJ | 1 MJ = 10⁶ J |
| Calorie | cal | 1 cal ≈ 4.184 J |
| Foot-pound force | ft·lbf | Common in US mechanical specs |
| Kilowatt-hour | kW·h | 1 kW·h = 3.6 × 10⁶ J |
Mass and height units
Mass accepts kg, g, lb, oz, metric tons (t), US short tons (sh tn), and UK long tons (lg tn). Height accepts meters, kilometers, feet, and miles. Enter vertical distance from your chosen reference—not total path length along a slope unless the problem defines h that way.
Planetary gravity reference
| Body | g (m/s²) | Notes |
|---|---|---|
| Earth | 9.81 | Classroom average; gn = 9.80665 m/s² |
| Moon | 1.62 | About 17% of Earth’s gravity |
| Mars | 3.71 | Common planetary comparison problem |
| Jupiter | 24.9 | Strongest g among major planets |
Gravity varies slightly with latitude and altitude on Earth. For homework, 9.81 m/s² is usually what your instructor expects unless the problem states otherwise. At the equator, gravity is closer to 9.78 m/s²; near the poles, about 9.83 m/s²—a small difference that matters only in precision labs, not most intro courses.
What counts as height (h)?
Measure vertical distance from your reference level straight up—not slope distance along a ramp unless the problem defines h that way. A book on a 2 m shelf has h = 2 m relative to the floor, regardless of how wide the shelf is.
Frequently Asked Questions
What is gravitational potential energy?
Energy stored because of an object’s position in a gravitational field. Higher above your reference level means more PEg, assuming the same mass and gravity.
What g should I use?
Use 9.81 m/s² for typical Earth problems. Standard gravity gn = 9.80665 m/s² appears in some precision contexts. For other bodies, pick a value from a planetary table or your assignment handout.
Which variable can this calculator solve for?
Any one of the four: PEg, m, g, or h. Enter the other three and press Calculate.
Can I mix unit systems?
Yes. Mass in pounds with height in feet and energy in joules works—the tool converts to SI before solving, then shows the answer in the unit you selected for the calculated variable.
What reference level should I use for height?
Potential energy is relative. Pick a zero point (ground, floor, table) and measure h vertically from there. Everyone on your team must use the same reference or answers will not match.
For motion energy at speed, use the Kinetic Energy Calculator. For spring storage, try the Elastic Potential Energy Calculator. For forces and acceleration, see the Force Calculator. Browse all physics calculators on RapidRatio.
Disclaimer. Informational only—not professional engineering or laboratory advice. Verify critical measurements with calibrated instruments and qualified analysis.