Potential and kinetic energy are the two main types of energy. Learn about potential energy, including its definition, units, examples, formulas, and how to calculate it.

### Potential Energy Definition

Potential energy is stored energy. The energy comes from an object’s relative position, its electric charge, internal stresses, or other factors. Because potential energy comes in many forms, it is further classified as elastic potential energy, chemical potential energy, nuclear potential energy, electric potential energy, gravitational potential energy, or magnetic potential energy. In formulas, potential energy is PE, U, or V. Potential energy depends on the observer’s frame of reference, so it is not invariant.

Potential energy does not depend on the path taken between maximum and minimum points. For example, you achieve the same potential energy if you hike a winding trail to the top of a mountain or if you get pulled straight up.

### Potential Energy Units

The SI unit for potential energy is the joule (J). One joule is one kg⋅m^{2}⋅s^{−2}. The English unit of kinetic energy is the foot-pound (ft⋅lb). Potential energy is a scalar quantity, which means it has magnitude and units, but no direction.

### Potential Energy Examples

There are many examples of potential energy in the everyday world. Remember, potential energy depends on relative position of objects, so you can’t just say “a ball has potential energy.” It has potential energy when a force can act upon it. So, raising a ball gives it energy due to the force of gravity. If the ball is an electron, it has potential energy when distanced from another charge due to the attractive and repulsive forces of protons and other electrons.

- A raised object, such as a book, weight, or apple
- A person at the top of a diving board
- An object at the top of a hill
- A stretched spring or rubber band
- A drawn bow
- Water at the top of a waterfall
- Water behind a dam
- A charged battery
- An explosive
- A chemical bond before it is broken
- Firewood, gasoline, and other fuels
- Food before you digest it
- A chemical hot pack or cold pack before you activate it
- A plugged-in appliance before you turn it on
- Two magnets held apart from each other
- An unstable atom before it decays or undergoes fission

### Potential Energy Formulas

There are multiple potential energy formulas. Which one you use depends on the type of potential energy in question.

**U = mgh**(gravitational), where m is mass, g is acceleration due to gravity, and h is height**U = 1/2 kx**(elastic, Hooke’s law), where k is the spring constant and x is the distance the spring is stretched^{2}**U = 1/2 CV**(electric), where C is the capacitance and V is the electric potential^{2}**U = -mB**(magnetic), where m is the magnetic moment and B is the magnetic field

### How to Calculate Potential Energy

The most common potential energy calculation is gravitational potential energy. For example, calculate the potential energy of a 68 kg person at the top of flight of stairs that is 3.2 meters above the ground. Assume acceleration due to gravity if 9.8 m/s^{2} (and realize it would be different on the Moon or Mars).

U = mgh

U = (68 kg)(9.8 m/s^{2})(3.2 m)

U = 2132.48 kg⋅m^{2}⋅s^{−2} = about 2132 J

### Potential vs Kinetic Energy

The sum of the potential plus kinetic energy is a constant, but each form converts into the other. For example, if you hold a ball above your head, it has potential energy relative to the ground. When you drop the ball, its potential energy decreases, but its kinetic energy increases. The ball has maximum kinetic energy when it strikes the ground, but zero potential energy. Similarly, a battery sitting on a shelf has potential energy. When you connect it to an object that draws power, some of the potential energy converts to kinetic electrical energy.

### References

- Feynman, Richard P. (2011). “Work and potential energy”. The Feynman Lectures on Physics, Vol. I. Basic Books. ISBN 978-0-465-02493-3.
- Goel, V. K. (2007).
*Fundamentals Of Physics*. Tata McGraw-Hill Education. ISBN 978-0-07-062060-5. - Serway, Raymond A.; Jewett, John W. (2004).
*Physics for Scientists and Engineers*(6th ed.). Brooks/Cole. ISBN 0-534-40842-7. - Tipler, Paul; Llewellyn, Ralph (2002).
*Modern Physics*(4th ed.). W. H. Freeman. ISBN 0-7167-4345-0.