Potential Energy Calculator

What is potential energy? – Definition

Potential energy is the energy of an object that is not in motion. Similar to kinetic energy, it can also be defined as the amount of work needed to lift an object to its height h. It can come from an object’s position in relation to other objects around it, stresses within the object and other factors. The official SI unit for it is J (joules).

William Rankine, a 19th century physicist and engineer, introduced the term we know today. However, the origin of the word dates back to Aristotle’s concept of potentiality. Potentiality and actuality are, in philosophy, two concepts used to analyze motion, causality, ethics and physiology.

Potential energy is closely linked to conservative forces. Conservative forces act on a body in such a way that all the work done by them depends on the starting and finishing positions of the body.

Types of energy

When talking about energy, we have two distinct types: kinetic and potential.

Kinetic energy is energy an object has while in motion. It is dependent on the object’s mass and velocity. For more information on this type of energy, check out our Kinetic Energy Calculator!

Potential energy also comes in multiple forms.

Types of potential energy

The different types of potential energy are:

• gravitational – related to gravity
• elastic – related to springs
• electric – related to electric fields
• chemical – related to the bonds in molecules
• nuclear – related to fusion and fission
• magnetic – related to magnets

We will be talking about the first type in this blog post.

As we said, gravitational potential energy depends on an object’s mass, as well as its distance from another object’s centre of mass. In classic mechanics, two or more objects that have mass always have a gravitational potential. For calculating the potential energy of two interacting particles, we use the following formula:

E_{p}= - \frac {G*m_{1}*m_{2}}{R}

G is the gravitational constant. For Earth, the gravitational constant is:

G= 6.67*10^{-11} \frac {Nm^{2}}{kg^{2}}

m₁ and m₂ are the masses of the two particles and R is their distance from one another.

The potential energy formula

However, when calculating the potential gravitational energy of an object that is elevated from the surface of the Earth, we use the following formula:

E_{p}= m*g*h

m is the mass of the object. g is the gravitational acceleration (9.81 m/s²) and h is the distance of the object from the surface. However, it is important to mention that we need to measure the height from the centre of the object’s mass.

In other words, while an object is above the ground, it has potential energy. Once it starts falling towards the ground, it gains kinetic energy.

How to calculate potential energy

As we said, in order to calculate it, we need to know the object’s mass (m), height (h), and the gravitational acceleration (g).

E_{p}= m*g*h

So, let’s say an object that has a mass of 5 kg is 10 m above the ground. Its potential energy will be:

E_{p}=5kg*9.80665 \frac {m}{s^{2}} *10m=490.3325J

If we want to calculate an object’s mass, using its potential energy, we can use the following formula:

m= \frac {E_{p}}{g*h}

So, if an object is 20 m above the ground, and its potential energy is 2500 J, its mass will be:

m= \frac {2500J}{9.80665\frac {m}{s^{2}}*20m}=12.75kg

Of course, the simplest way to calculate this type of potential energy is to use our calculator, which you can find above this. For conversion between different energy types, head to this Energy Conversion tool.

Potential energy examples

When it comes to gravitational potential energy, we encounter it basically every day. Essentially, any object that is not in motion, but has the potential to start moving has potential energy. So, any object that is near an edge, and is about to fall, such as a book on a table. A ripe fruit that is ready to disconnect from its branch and fall to the ground has gravitational potential energy.

The concept is similar for elastic potential energy, except it is, logically, connected to elasticity. This appears in things such as springs, rubber bands, and elastic balls, when they are stretched out. Obviously, a golf ball is less elastic than a ping pong ball, even though they are the same size. Because of this, when you drop them from the same height, the ping pong ball will bounce much higher.

Chemical potential energy appears when a strong chemical reaction is about to happen. For example, a fire getting lit, a bullet being fired from a gun or iron right as it’s about to corrode, all contain chemical potential energy.

For electric potential energy, look no further than the electronic devices around you. Your phone, your TV, or an LED flashlight right before you turn them on, all have electric potential energy. However, a charged battery doesn’t contain electric, but instead contains chemical potential energy.

Nuclear potential energy is contained within an atom. Once the atom is split open (fission), or is combined with another atom (fusion), that energy is released, and turns into kinetic energy. Fission releases massive amounts of energy, and is used in nuclear power plants.

Magnetic potential energy is present when an object interacts with a magnetic force. Essentially, any metal that can stick to magnets, contains magnetic potential energy.

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