Potential Energy Calculator
Calculate gravitational potential energy from mass, height, and gravitational acceleration using PE = mgh. Also shows the equivalent velocity if the object were to fall. See also our Kinetic Energy Calculator and Force Calculator.
How to Calculate Potential Energy
Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. When you lift an object against gravity, you do work on it, and that work is stored as potential energy. When the object is released, this stored energy converts to kinetic energy as it falls. This interplay between potential and kinetic energy is fundamental to understanding mechanics, from simple pendulums to hydroelectric power generation.
To calculate gravitational potential energy, multiply the mass of the object by the gravitational acceleration and the height above a reference point: PE = mgh. The reference point (where PE = 0) is arbitrary — you can choose the ground, a tabletop, or any convenient level. What matters physically is the change in potential energy between two positions, not the absolute value.
The standard gravitational acceleration on Earth's surface is 9.81 m/s², but this varies slightly with latitude and altitude. At the equator, g ≈ 9.78 m/s²; at the poles, g ≈ 9.83 m/s². On the Moon, g ≈ 1.62 m/s²; on Mars, g ≈ 3.72 m/s². For most calculations on Earth's surface, 9.81 m/s² is sufficiently accurate.
Potential Energy Formula
Gravitational PE (near surface):
PE = mgh
m = mass (kg), g = gravity (m/s²), h = height (m)
Gravitational PE (general):
PE = -GMm/r
G = 6.674×10⁻¹¹ N⋅m²/kg²
Elastic PE (spring):
PE = ½kx²
k = spring constant, x = displacement
Conservation of Energy:
PE₁ + KE₁ = PE₂ + KE₂ (no friction)
mgh = ½mv² (falling from rest)
v = √(2gh) (velocity after falling height h)
Example Calculation
A 10 kg object is held at a height of 5 meters above the ground. Calculate its potential energy:
Given: m = 10 kg, h = 5 m, g = 9.81 m/s²
PE = mgh = 10 × 9.81 × 5 = 490.5 J
If dropped, velocity at ground:
v = √(2gh) = √(2 × 9.81 × 5) = √98.1 = 9.905 m/s
= 35.66 km/h
Verify with KE at ground:
KE = ½mv² = ½ × 10 × 9.905² = 490.5 J ✓
PE at top = KE at bottom (energy conserved)
Potential Energy Reference Table
| Mass (kg) | Height (m) | Gravity (m/s²) | PE (J) |
|---|---|---|---|
| 0.1 kg | 1 m | 9.81 | 0.981 J |
| 1 kg | 1 m | 9.81 | 9.81 J |
| 1 kg | 10 m | 9.81 | 98.1 J |
| 5 kg | 2 m | 9.81 | 98.1 J |
| 10 kg | 5 m | 9.81 | 490.5 J |
| 50 kg | 3 m | 9.81 | 1471.5 J |
| 70 kg | 10 m | 9.81 | 6867 J |
| 80 kg | 100 m | 9.81 | 78480 J |
| 500 kg | 50 m | 9.81 | 245250 J |
| 1000 kg | 10 m | 9.81 | 98100 J |
| 1000 kg | 100 m | 9.81 | 981000 J |
| 10000 kg | 200 m | 9.81 | 19620000 J |
Frequently Asked Questions
What is gravitational potential energy?
Gravitational potential energy is the energy stored in an object due to its elevated position in a gravitational field. It equals the work done against gravity to raise the object to that height: PE = mgh. This energy is "potential" because it has the potential to be converted to kinetic energy (motion) when the object is released. It is measured in joules (J).
Why is the reference point for PE arbitrary?
Only changes in potential energy have physical significance, not absolute values. Setting PE = 0 at ground level is convenient but not required — you could set it at a tabletop, basement floor, or sea level. The physics depends on ΔPE = mg(h₂-h₁), which is the same regardless of where you define zero. Choose the reference point that simplifies your calculation.
Can potential energy be negative?
Yes, if the object is below your chosen reference point. If you set PE = 0 at ground level, an object in a basement has negative PE. In orbital mechanics, PE = -GMm/r is always negative (with PE = 0 at infinity), and objects are bound when their total energy (KE + PE) is negative. Negative PE simply means the object is below the reference level.
How does PE relate to hydroelectric power?
Hydroelectric dams convert gravitational PE of water into electrical energy. Water stored at height h has PE = mgh per unit mass. As it flows down through turbines, PE converts to KE of the water, then to rotational KE of the turbine, then to electrical energy. A dam with 100m head and 1000 kg/s flow rate generates: P = ṁgh = 1000 × 9.81 × 100 = 981 kW (before efficiency losses).
What is the difference between PE = mgh and PE = -GMm/r?
PE = mgh is an approximation valid near Earth's surface where g is approximately constant. PE = -GMm/r is the exact formula for any distance from a massive body. Near the surface, the change in -GMm/r over small height changes equals mgh. Use mgh for everyday calculations (buildings, hills). Use -GMm/r for orbital mechanics, escape velocity, and large altitude changes where g varies significantly.
What other types of potential energy exist?
Besides gravitational PE, common types include: elastic PE (½kx² in springs and deformed materials), electrical PE (qV in electric fields, kq₁q₂/r between charges), chemical PE (stored in molecular bonds — released in combustion, batteries), nuclear PE (binding energy in atomic nuclei — released in fission/fusion), and magnetic PE (in magnetic fields). All represent stored energy that can be converted to other forms.
Energy Storage Applications
Gravitational potential energy is used for large-scale energy storage in pumped-storage hydroelectric facilities. During low-demand periods, excess electricity pumps water uphill to a reservoir. During peak demand, the water flows back down through turbines to generate electricity. This is currently the largest form of grid-scale energy storage worldwide, with round-trip efficiencies of 70-85%. New concepts include using heavy weights in mine shafts or stacking concrete blocks as alternatives to water-based systems.
Gravity on Different Celestial Bodies
The gravitational acceleration varies significantly across celestial bodies, directly affecting potential energy calculations. Earth: 9.81 m/s², Moon: 1.62 m/s² (16.5% of Earth), Mars: 3.72 m/s² (37.9%), Jupiter: 24.79 m/s² (253%), Sun: 274 m/s² (2793%). An object at 10m height on the Moon has only 16.5% of the PE it would have at the same height on Earth. This affects everything from how high astronauts can jump to the energy requirements for launching rockets.