Gravitational Potential Energy Calculator – PE = m·g·h (All Units)
Potential Energy (PE)
Earth: 9.8 m/s², Moon: 1.62 m/s², Mars: 3.71 m/s²
Enter mass, height, and gravity (any units), then click "Calculate PE".
Example: 10 kg × 9.8 m/s² × 5 m = 490 J
The Gravitational Potential Energy Calculator computes $PE = m \cdot g \cdot h$ using any combination of units. It supports mass units (kg, g, mg, tonne, lb, oz, stone, US/UK ton), height units (m, cm, mm, km, in, ft, yd, mi), gravity units (m/s², cm/s², mm/s², ft/s², in/s², G), and output energy units (J, kJ, MJ, Wh, kWh, cal, kcal, eV). All inputs are automatically converted to SI units for accurate calculations.
Gravitational Potential Energy Formula
PE = m · g · h
The calculator converts every input to base SI units (kg, m, m/s²), computes the energy in Joules, and then converts to your chosen output unit. This ensures maximum flexibility without compromising accuracy.
Applications
Physics: Energy conservation, work‑energy theorem, mechanics.
Engineering: Dam design, cranes, roller coasters.
Astrophysics: Comparing planets, orbital mechanics.
Understanding Potential Energy
Potential energy is energy stored due to height. Work done against gravity becomes PE. The reference level (h=0) is arbitrary; only differences matter. This calculator handles any unit system.
Celestial Bodies Gravitational Acceleration & Potential Energy Comparison Reference Table
Celestial Body
Surface Gravity (g)
PE for 10 kg at 10 m (Joules)
PE in Kilojoules (kJ)
Gravity Ratio vs Earth
Sun
274.0 m/s²
27,400 J
27.40 kJ
27.94x
Jupiter
24.79 m/s²
2,479 J
2.479 kJ
2.53x
Neptune
11.15 m/s²
1,115 J
1.115 kJ
1.14x
Earth (Standard)
9.80665 m/s²
980.67 J
0.981 kJ
1.00x
Venus
8.87 m/s²
887.0 J
0.887 kJ
0.90x
Mars
3.72 m/s²
372.0 J
0.372 kJ
0.38x
Moon
1.62 m/s²
162.0 J
0.162 kJ
0.165x
Pluto
0.62 m/s²
62.0 J
0.062 kJ
0.063x
Derivation of Gravitational Potential Energy
The gravitational potential energy near the Earth's surface is derived from the work done against gravity. When an object of mass $m$ is lifted to a height $h$, the force required is equal to its weight $mg$, directed opposite to gravity. The work done is $W = F \cdot d = mg \cdot h$. This work is stored as potential energy: $PE = mgh$. This derivation assumes constant gravity (valid for small heights compared to Earth's radius). For larger distances, the inverse‑square law must be used with the general formula PE = -G*M*m/r, but the near‑surface approximation $mgh$ works perfectly in everyday situations.
Real‑World Examples
Hydroelectric Dams: Water stored behind a dam has high gravitational potential energy. When released, it converts to kinetic energy, spinning turbines to generate electricity.
Roller Coasters: The first hill lifts cars to a high point, giving them maximum PE. This PE converts to kinetic energy as they descend, powering the rest of the ride.
Pendulums: At the highest point, a pendulum has maximum PE and minimum speed; at the bottom, PE is minimum and kinetic energy is maximum.
Human Power: Lifting a weight, climbing stairs, or jumping all involve converting chemical energy into gravitational potential energy.
Common Misconceptions About Potential Energy
"Potential energy is absolute" – No, only differences in PE matter. The zero point (height reference) can be chosen arbitrarily.
"Heavier objects always have more PE at the same height" – Yes, because PE = mgh, but that does not mean they fall faster (acceleration due to gravity is independent of mass).
"Potential energy is only stored in vertical motion" – Correct; horizontal movement against no force does not change gravitational PE.
"Work done equals change in PE only if no other forces act" – Work done by gravity equals minus the change in PE, but if other forces (like friction) are present, total work does not equal ΔPE.
Why Convert Units for Potential Energy?
Engineers and scientists work in different unit systems (metric, imperial, etc.). Converting units correctly is critical to avoid costly mistakes. For example, a NASA Mars orbiter was lost because one team used metric newtons and another used imperial pounds. Our calculator handles all conversions automatically using internationally recognised standard factors, so you never have to worry about unit errors when computing gravitational potential energy.
Use this gravitational potential energy calculator for homework, engineering design, or curiosity. Experiment with different units and see how energy scales with mass, height, and gravity. The step‑by‑step breakdown helps you learn the physics behind every calculation.
Frequently Asked Questions about Gravitational Potential Energy
What units can I use in this gravitational potential energy calculator?
Mass: kg, g, mg, tonne, lb, oz, stone, US/UK ton. Height: m, cm, mm, km, in, ft, yd, mi. Gravity: m/s², cm/s², mm/s², ft/s², in/s², G. Energy output: J, kJ, MJ, Wh, kWh, cal, kcal, eV.
What is standard gravity on Earth?
Standard gravitational acceleration on Earth is 9.80665 m/s² (often rounded to 9.8 m/s² or 32.174 ft/s²).
How is Gravitational Potential Energy derived?
PE is derived from work done against gravity: W = F × d = (m × g) × h = mgh.
What is the difference between Kinetic Energy and Potential Energy?
Potential energy is stored energy due to an object's position or height. Kinetic energy is energy possessed by an object due to its motion (KE = 0.5 * m * v²).
Does gravitational potential energy depend on the reference level?
Yes. Height h is measured relative to an arbitrary reference plane (e.g. ground level, sea level, or floor). Only the difference in PE matters in physical applications.
What is the gravitational potential energy on the Moon vs Earth?
Because lunar gravity (1.62 m/s²) is approximately 1/6th of Earth's gravity (9.80665 m/s²), an object at height h on the Moon possesses only ~16.5% of its potential energy on Earth.
How does PE = mgh convert to Joules?
When mass is in kilograms (kg), gravity in meters per second squared (m/s²), and height in meters (m), the resulting product 1 kg·m²/s² is exactly equal to 1 Joule (J).
When does the simple PE = mgh formula break down?
PE = mgh assumes constant gravitational acceleration g. For celestial objects or satellites far above Earth's surface (where gravity varies with distance), the general gravitational potential energy formula PE = -G*M*m/r must be used.