Potential Energy: What Is It & Why It Matters (W/ Formula & Examples)

All physics students have potential – potential energy, that is. But those who take the time to determine what that means in terms of physics will have ​more potential​ to affect the world around them than those who don't. At the very least, they will be able to reply knowingly to a nagging adult with an internet meme quip: "I'm not lazy, I'm overflowing with potential energy."

The concept of potential energy might seem confusing at first. But in short, you can think of potential energy as stored energy. It has the ​potential​ to transform into motion and make something happen, like a battery that is not yet connected or a plate of spaghetti that a runner is about to eat the night before the race.

Potential energy is one of three broad categories of energy found in the universe. The other two are kinetic energy, which is the energy of motion, and thermal energy, which is a special, non-reusable type of kinetic energy.

Without potential energy, no energy could be saved for later use. Fortunately, plenty of potential energy does exist, and it is constantly converting back and forth between itself and kinetic energy, making stuff happen.

With each transformation, some potential and kinetic energy transforms into thermal energy, also known as heat. Eventually, all the universe's energy will be converted to thermal energy, and it will experience "heat death," when no more potential energy exists. But until that far-off future time, potential energy will keep the possibilities for action open.

The SI unit for potential energy, and any for of energy for that matter, is the joule, where 1 joule = 1 (newton)(meter).

There are many types of potential energy. Among these forms of energy are:

​Mechanical potential energy:​ Also known as gravitational potential energy, or GPE, this refers to energy stored by an ​object's position relative to a gravitational field, such as that near the Earth's surface​.

For example, a book sitting at the top of a shelf has the potential to fall down due to the force of gravity. The higher it is in relation to the ground – and thereby in relation to the Earth, the source of the gravitational field – the longer a fall it has the potential to traverse. More on this later.

​Chemical potential energy:​ Energy stored in molecular bonds is chemical energy. It can be released and transformed into kinetic energy by breaking bonds. ​Hence, the more bonds in a molecule, the more potential energy it contains.​

For example, when eating food, the process of digestion breaks down molecules of fats, proteins, carbohydrates or amino acids so that the body can use that energy to move. Because fats are the longest of those molecules with the most bonds between atoms, they store the most energy.

Similarly, the logs used in a campfire contain chemical potential energy that is released when they are burned and the bonds between molecules in the wood are broken. Anything that requires a chemical reaction to "go" – including using batteries or burning gasoline in a car – contains chemical potential energy.

​Elastic potential energy:​ This form of potential energy is the energy stored in the deformation of an object from its normal shape. When an object is stretched or compressed from its original shape – say a rubber band pulled out or a spring held in a tight coil – it has the ​potential​ to spring or bounce back when released. Or, a squishy couch cushion is pressed with the imprint of someone sitting on it so that, when they stand, the imprint slowly rises back until the couch looks as it did before they sat.

​Nuclear potential energy:​ A lot of potential energy is stored by the nuclear forces holding atoms together. For instance, the strong nuclear force inside a nucleus holding the protons and neutrons in place. This is why it is so hard to split atoms, a process that only happens in nuclear reactors, particle accelerators, the centers of stars or other high energy situations.

Not to be confused with chemical potential energy, nuclear potential energy is stored ​inside individual atoms​. As their name states, atomic bombs represent one of humanity's most aggressive uses of nuclear potential energy.

​Electric potential energy:​ This energy is stored by holding electric charges in a particular configuration. For instance, when a sweater that has a lot of built-up negative charges is brought close to a positive or neutral object, it has the ​potential​ to cause motion by attracting positive charges and repelling other negative charges.

Any single charged particle held in place in an electric field also has electric potential energy. This example is analogous to gravitational potential energy in that the charge's position in relation to the electric field is what determines its amount of potential energy, just like an object's position in relation to the gravitational field determines its GPE.

Gravitational potential energy, or GPE, is one of the few types of energy for which high school physics students typically perform calculations (others are linear and rotational kinetic energy). It results from the gravitational force. The variables that affect how much GPE an object has are mass ​m,​ the acceleration due to gravity ​g​, and height ​h.​

\(GPE=mgh\)

Where GPE is measured in joules (J), mass in kilograms (kg), acceleration due to gravity in meters per second per second (m/s²) and height in meters (m).

Note that on Earth, ​g​ is treated as always equal to 9.8 m/s². In other locations where Earth is not the local source of gravitational acceleration, such as on other planets, ​g​ has other values.

The formula for GPE implies that the more massive an object is or the higher it is placed, the more potential energy it contains. This in turn explains why a penny dropped from the top of a building will be going much faster at the bottom than one dropped from a person's pocket right above the sidewalk. (This is also an illustration of the conservation of energy: as the object falls, its potential energy decreases, so its kinetic energy must increase by the same amount in order for the total energy to remain constant.)

Starting at a higher height means the penny will accelerate downwards over a longer distance, resulting in a faster speed by the end of the trip. Or, to keep moving over a longer distance, the penny on the roof must have started with more potential energy, which the GPE formula quantifies.

Rank the following objects from most to least gravitational potential energy:

•A 50-kg woman at the top of a 3-m ladder
•A 30-kg moving box at the top of a 10-m landing
•A 250-kg barbell held 0.5 m above the head of a power lifter

To compare these, calculate GPE for each situation using the formula GPE = mgh.

•Woman GPE = (55 kg)(9.8 m/s²)(3 m) = 1,617 J
•Moving box GPE = (30 kg)(9.8 m/s²)(10 m) = 2,940 J
•Barbell GPE = (250 kg)(9.8 m/s²)(0.5 m) = 1,470 J

So, from most to least GPE the order is: moving box, woman, barbell.

Note that, mathematically, since all the objects were on Earth and had the same value for ​g​, leaving that number out would still result in the correct order (but doing so would ​not​ give the actual amounts of energy in joules!).

Consider instead that the moving box was on Mars instead of Earth. On Mars, the acceleration due to gravity is roughly one-third what it is on Earth. That means the moving box would have about one-third the amount of GPE on Mars at 10 m high, or 980 J.