🎯 Solve for:
Enter mass.
Enter height.
Enter PE.
Stiffness of the spring
Enter spring constant.
Extension or compression from equilibrium
Enter displacement.
Or solve for k or x instead
Potential Energy
—
💡
ℹ️ PE = mgh assumes uniform gravitational field and negligible air resistance. The reference point (h = 0) is arbitrary — only changes in PE have physical meaning.
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Sources & Methodology
Formulas and gravity values per NIST and Serway & Jewett Physics for Scientists and Engineers.
Serway & Jewett — Physics for Scientists and Engineers, 10th Ed.
Standard reference for gravitational PE, elastic PE, conservation of energy, and work-energy theorem.
NIST — Standard Acceleration of Gravity
g = 9.80665 m/s² (standard gravity by definition). physics.nist.gov
NASA — Planetary Fact Sheets
Surface gravity values for Moon, Mars, Jupiter, Venus, and Mercury. NASA Planetary Fact Sheets
Gravitational PE = m x g x h [SI: kg, m/s², m, joules]
Elastic PE = (1/2) x k x x² [k in N/m, x in m, PE in joules]
Free-fall velocity from height h: v = sqrt(2gh)
Conservation: KE + PE = constant (no friction)
Elastic PE = (1/2) x k x x² [k in N/m, x in m, PE in joules]
Free-fall velocity from height h: v = sqrt(2gh)
Conservation: KE + PE = constant (no friction)
PE = m × g × h
Example: 5 kg book on a 2 m shelf on Earth (g = 9.807 m/s²).
PE = 5 × 9.807 × 2 = 98.07 J
If it falls: all PE converts to KE at floor level.
v = sqrt(2gh) = sqrt(2 × 9.807 × 2) = 6.26 m/s
PE = 5 × 9.807 × 2 = 98.07 J
If it falls: all PE converts to KE at floor level.
v = sqrt(2gh) = sqrt(2 × 9.807 × 2) = 6.26 m/s
Last reviewed: April 2026
How Is Potential Energy Calculated?
Gravitational potential energy (GPE) is stored energy due to an object's position in a gravitational field. When a mass is lifted to a height h above a reference level, work is done against gravity equal to W = mgh. This work is stored as potential energy, ready to be converted to kinetic energy when the object falls.
The reference level (PE = 0) is arbitrary — you choose it. Often it's the ground, the floor, or the lowest point of motion. Only changes in potential energy have physical meaning. GPE depends linearly on both mass and height.
Surface Gravity on Different Planets
| Body | g (m/s²) | PE ratio (vs Earth) | Free-fall from 10 m |
|---|---|---|---|
| Earth | 9.807 | 1.00× | 14.0 m/s |
| Moon | 1.62 | 0.17× | 5.69 m/s |
| Mars | 3.72 | 0.38× | 8.63 m/s |
| Venus | 8.87 | 0.90× | 13.3 m/s |
| Jupiter | 24.79 | 2.53× | 22.3 m/s |
💡 Conservation of Mechanical Energy: When only gravity acts (no friction or air resistance), total mechanical energy is constant: KE + PE = constant. A ball thrown upward converts KE to PE as it rises, then PE back to KE as it falls. At the highest point, all energy is PE; at the lowest, all is KE. This allows calculating maximum height or impact velocity from initial conditions.
Frequently Asked Questions
GPE = mgh. m = mass (kg), g = gravity (m/s²), h = height above reference (m). Unit: joules. It is the energy stored in an object due to its position in a gravitational field.
Gravitational: PE = mgh. Elastic: PE = ½kx² (k = spring constant, x = displacement). Electric: PE = kq¹q²/r (Coulomb's law).
PE = m × g × h. Example: 5 kg at 2 m on Earth: PE = 5 × 9.807 × 2 = 98.07 J.
g = 9.80665 m/s² (NIST standard). Often approximated as 9.81 m/s². Ranges from ~9.78 (equator) to ~9.83 (poles) due to Earth's shape and rotation.
PE is directly proportional to height. Doubling height doubles PE (at the same mass and g). Tripling height triples PE. PE = 0 at the chosen reference level.
PE = ½kx². k = spring constant (N/m), x = displacement from equilibrium (m). Energy stored in a stretched/compressed spring. Doubles when displacement doubles? No — it quadruples (x²).
mgh = ½mv² (no air resistance). Solving for velocity: v = sqrt(2gh). A 10 m fall: v = sqrt(2 × 9.807 × 10) = 14.0 m/s. Mass cancels — all objects fall at the same speed regardless of weight.
The reference level (PE = 0) is chosen by the problem solver — commonly ground level or the lowest point of motion. Only changes in PE have physical meaning, not absolute values.
On the Moon, g = 1.62 m/s² (about 1/6 of Earth). A 5 kg object at 2 m: PE = 5 × 1.62 × 2 = 16.2 J (vs 98 J on Earth). Astronauts can jump 6× higher on the Moon.
PE = stored energy of position. KE = energy of motion. They interconvert: falling objects convert PE to KE. A pendulum swings PE ↔ KE. Total mechanical energy KE + PE = constant (no friction).
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