Potential energy is energy stored in an object or system because of its position relative to other objects or because its particles are arranged in a particular way. A book on a shelf, water held behind a dam, a drawn bow, and a battery all have the potential to change—and to release energy in the process. That is why potential energy is often called stored energy: it describes what a system can do if its position or configuration changes.
Potential energy describes what a system can do next
The concept of potential energy is defined by relationships. Gravity links a book and Earth; electric forces link charges; forces between atoms shape a stretched spring. For that reason, gravitational potential energy belongs to the book–Earth system, not to a book in isolation.
Physicists commonly write potential energy as PE, U, or V. Scottish engineer and physicist William Rankine coined the term in 1853. The useful idea behind it is older: a system can have a stored capability even while nothing is moving.
Potential energy is only defined for conservative forces. With such a force, the total work done depends on the starting and ending positions, not on the route between them. Gravity near Earth is the familiar example: lifting an object around a curved path to the same final height gives the same change in potential energy as lifting it straight up.
Gravitational potential energy makes height measurable
Near Earth’s surface, gravitational potential energy is calculated with PE = mgh. Here, m is mass in kilograms, g is 9.8 m/s², and h is height in meters above a chosen reference level. The SI unit is the joule (J), where 1 J = 1 N·m = 1 kg·m²·s⁻².
| Quantity | Value | Meaning |
|---|---|---|
| m | 10 kg | Mass of the object |
| g | 9.8 m/s² | Acceleration due to gravity near Earth |
| h | 5 m | Height above the reference level |
| PE | 490 J | (10 kg)(9.8 m/s²)(5 m) |
A 10 kg object raised 5 m therefore gains 490 J. The number tells you the difference in potential energy between its two heights. For a roller-coaster cart with a mass of 300 kg at 25 m (with g = 9.81 m/s²), the value relative to the ground is 7.36 × 10⁴ J. If it descends to 7 m with friction neglected, 5.30 × 10⁴ J is converted into kinetic energy.
A reference point explains why potential energy can be negative
Potential energy can be positive, negative, or zero. The chosen zero level sets the sign. If ground level is zero, a ball in a hole below ground can have negative gravitational potential energy.
Only a difference in potential energy, written ΔPE, has physical significance. The general gravitational formula for masses M and m separated by distance r is U = −GMm/r. It is negative when zero is defined at infinite separation, and it approaches zero as r approaches infinity.
The main types of potential energy begin with position and arrangement
The forms of potential energy differ by the force and arrangement involved.
- Gravitational potential energy: energy due to height in a gravitational field. Water behind a dam flows downward, turns turbines, and produces electricity.
- Elastic potential energy: energy in something stretched or compressed, including a rubber band, bent bow limb, trampoline, pogo stick, or suspension spring. It arises ultimately from electromagnetic forces between atoms and molecules.
- Chemical potential energy: energy stored in the bonds between atoms and molecules. Food, batteries, biomass, petroleum, natural gas, and coal are examples.
- Electrical potential energy: energy associated with the relative positions of electric charges. For point charges, UE = keqQ/r. A charged capacitor stores UE = ½CV² = Q²/(2C).
- Nuclear potential energy: energy in an atom’s nucleus from the strong nuclear force binding protons and neutrons. The Sun releases energy when four hydrogen nuclei combine into helium, about 26.73 MeV per reaction.
Elastic potential energy shows why springs push back
For a spring, elastic potential energy is PEel = ½kx². The spring constant k, measured in N/m, describes stiffness; x is displacement from equilibrium in meters. Hooke’s law, F = −kx, says the restoring force points back toward the original shape and grows linearly with displacement.
A spring with k = 50.0 N/m compressed by 0.150 m stores 0.563 J. In a tranquilizer gun example, that amount launches a dart at over 80 km/h. A bow with k = 575 N/m drawn 0.400 m stores 46.0 J. The squared x term matters: doubling the draw distance makes the stored spring energy four times as large.
Chemical potential energy powers batteries, bodies, and fires
Chemical potential energy is stored in bonds, held by the electric attraction between electrons and nuclei in specific configurations. In a AA battery, a chemical reaction between zinc and manganese dioxide releases energy as electrical energy. Burning wood or combusting gasoline changes chemical energy into thermal energy.
Food provides another daily example. Bodies convert its chemical potential energy into mechanical energy for muscle contraction and thermal energy. At a larger scale, combusting 1 barrel, or 159 L, of petroleum releases roughly 6 GJ of chemical energy. Coal, petroleum, and natural gas come from buried plants and microorganisms transformed over millions of years.
Potential energy and kinetic energy trade places as systems change
Unlike potential energy, kinetic energy is the energy of motion: KE = ½mv². A pendulum at the highest point of its swing has maximum potential energy and zero kinetic energy. At the bottom, its kinetic energy is maximum and its potential energy is minimum.
The same exchange appears when a book falls. Its gravitational potential energy becomes kinetic energy; on impact, that kinetic energy becomes heat, deformation, and sound. In an ideal roller coaster without friction, the relationship is KE₁ + PE₁ = KE₂ + PE₂. A skateboarder in a half-pipe similarly speeds up while descending and slows while climbing as energy changes form.
Real systems include friction and air resistance. A pendulum eventually stops because non-conservative work converts mechanical energy into thermal energy, not because energy disappears. Energy cannot be created or destroyed; it can only be transformed.
Common misconceptions hide the most important details
- “Potential energy is always positive.” No. Its sign depends on the reference point; changes are what can be measured.
- “A single object owns gravitational potential energy.” Not quite. It is a property of an interacting system, such as object and Earth.
- “Stored means motion can never be involved.” A system may have both types at once. A moving roller-coaster cart can still be above its reference height.
- “All stored energy becomes useful motion.” Friction, deformation, and sound can redirect part of the energy into other forms.
Frequently Asked Questions
What is potential energy called?
Potential energy is often called stored energy because it is associated with position or configuration and can be transformed when the system changes.
How do you explain potential energy simply?
Think of a book held above the floor or a stretched rubber band. Neither must be moving, but each can change in a way that releases energy.
What are some examples of potential energy in daily life?
Water behind a dam, a high shelf book, a compressed spring, a drawn bow, food, and a battery are everyday examples.
How is gravitational potential energy calculated?
Near Earth, use PE = mgh: multiply mass in kilograms by 9.8 m/s² and height in meters relative to a chosen reference level.
What is the difference between potential energy and kinetic energy?
Potential energy comes from position or configuration; kinetic energy comes from motion. A falling book converts the first into the second.
Why does potential energy depend on a reference point?
The zero level is chosen for convenience, so an absolute value can change with the reference. The measurable quantity is the difference between two positions or configurations.
