Potential Energy Calculator
Calculate gravitational potential energy from mass, height and gravity, or flip the calculator around to solve for the mass, height or gravity that gives a target energy. Pick a planet or Moon for g, switch between metric and imperial units, and see the energy in joules along with everyday equivalents and the speed the object would reach if it fell.
Formula
Worked example
2 kg lifted to 10 m on Earth (g = 9.807): PE = 2 × 9.807 × 10 = 196.1 J, about 0.0469 kcal, and it would hit the ground at √(2 × 9.807 × 10) ≈ 14.0 m/s.
How the calculation works
The calculator applies the classical gravitational potential energy relation, where PE is the product of an object's mass, the local gravitational acceleration, and its height above the chosen reference point. All three variables contribute linearly, so doubling any one of them doubles the result. The default gravitational acceleration is 9.81 m/s², the standard value adopted by the International Bureau of Weights and Measures (BIPM) for sea-level calculations on Earth.
How to use this calculator
Enter the object's mass in kilograms and its height in metres above your chosen reference level, that level can be the ground, a table, or any convenient baseline, as long as you apply it consistently. If you are working somewhere other than sea level, or on another planet, replace the default g value with the appropriate local gravitational acceleration. The result appears in joules (J), the SI unit of energy.
What affects the result
Local gravitational acceleration varies with latitude and altitude: at the poles it reaches roughly 9.83 m/s², while at the equator it falls to about 9.78 m/s². Elevation above sea level reduces g by approximately 0.003 m/s² per kilometre of altitude. For everyday engineering and classroom problems the 9.81 m/s² standard value introduces negligible error, but high-precision work, such as gravimetry or satellite trajectory analysis, requires a measured local value of g.
Limitations to keep in mind
This calculator models gravitational potential energy only in the Newtonian, uniform-field approximation, which holds well near Earth's surface but breaks down over large vertical distances where g changes appreciably. It does not account for elastic potential energy, electric potential energy, or any other form of stored energy. The reference height is arbitrary; only differences in potential energy between two positions carry physical meaning, so the absolute number the calculator returns is meaningful only relative to the baseline you define.
Reverse solving and unit switches
Use the "Solve for" selector to work backwards. Choose Mass, Height or Gravity, enter the target potential energy in joules along with the two known quantities, and the calculator rearranges PE = m·g·h to return the missing value. Mass can be entered in kilograms, grams, pounds, ounces or tonnes, and height in metres, centimetres, feet, inches, kilometres or miles; everything is converted to SI internally so the joule result is always correct. Pick a planet, the Moon or the Sun from the gravity source list to use that body's surface gravity, or select Custom g to type your own value for a specific latitude or altitude.
Energy equivalents and free-fall speed
Alongside the result in joules, the calculator converts the energy into kilocalories, watt-hours and foot-pounds so you can compare it to everyday quantities. It also reports the impact speed the object would reach if it fell from that height back to the reference level, found from conservation of energy: at the bottom all of the potential energy has become kinetic energy, so ½·m·v² = m·g·h and v = √(2·g·h). This links the stored energy directly to motion and is handy for drop tests, roller-coaster problems and free-fall questions.
Surface gravity by celestial body
| Body | Gravity (m/s²) | Relative to Earth |
|---|---|---|
| Sun | 274 | 27.9x |
| Jupiter | 24.79 | 2.53x |
| Neptune | 11.15 | 1.14x |
| Saturn | 10.44 | 1.06x |
| Earth | 9.807 | 1.00x |
| Venus / Uranus | 8.87 | 0.90x |
| Mars | 3.71 | 0.38x |
| Mercury | 3.70 | 0.38x |
| Moon | 1.62 | 0.17x |
Approximate surface gravitational acceleration. The same lift stores energy in proportion to g.
Frequently asked questions
What units does the calculator return, and why?
The result is given in joules (J), the SI unit of energy. One joule equals one kilogram times one metre squared per second squared (kg·m²/s²), which follows directly from multiplying kilograms, metres per second squared, and metres together in the potential energy formula.
Can I use this calculator for objects on the Moon or Mars?
Yes. Replace the default g value with the appropriate surface gravity: approximately 1.62 m/s² for the Moon and 3.72 m/s² for Mars. All other inputs remain in the same SI units, so the output is still valid in joules.
Why does the choice of reference height not matter for most problems?
Potential energy is defined relative to an arbitrary baseline, so only the change in PE between two positions is physically significant, not the absolute value. When solving problems involving falling objects, projectiles, or roller coasters, you subtract the initial and final PE values, and the reference level cancels out exactly.
Can I find the mass or height for a target potential energy?
Yes. Set "Solve for" to Mass, Height or Gravity, then enter the potential energy you want in joules plus the two values you already know. The calculator rearranges PE = m·g·h (so m = PE / (g·h), h = PE / (m·g), or g = PE / (m·h)) and returns the missing quantity, with the full rearrangement shown in the steps panel.
How fast will the object be moving when it lands?
In free fall with no air resistance, all of the potential energy becomes kinetic energy at the bottom, so ½·m·v² = m·g·h. Solving for speed gives v = √(2·g·h), which the calculator reports as the impact speed. The mass cancels out, so a heavy and a light object dropped from the same height reach the same speed.