Potential Energy Calculator

Calculate gravitational and elastic potential energy.

Select the type of potential energy and enter the required values.

Examples

Load an example to see how the calculator works.

Book on a Shelf

gravitational

A 2 kg book placed on a shelf 1.5 meters high.

Type: Gravitational

Mass: 2 kg, Height: 1.5 m, Gravity: 9.81 m/s²

Car on a Hill

gravitational

A 1500 kg car at the top of a 50-meter hill.

Type: Gravitational

Mass: 1500 kg, Height: 50 m, Gravity: 9.81 m/s²

Compressed Spring

elastic

A spring with a constant of 400 N/m is compressed by 0.2 meters.

Type: Elastic

Spring Constant: 400 N/m, Displacement: 0.2 m

Stretched Bungee Cord

elastic

A bungee cord with a spring constant of 100 N/m is stretched by 10 meters.

Type: Elastic

Spring Constant: 100 N/m, Displacement: 10 m

Other Titles
Understanding the Potential Energy Calculator: A Comprehensive Guide
An in-depth look at the principles of potential energy, its types, and applications.

What is Potential Energy?

  • The Concept of Stored Energy
  • Gravitational Potential Energy (GPE)
  • Elastic Potential Energy (EPE)
Potential energy is the stored energy an object possesses due to its position or configuration. It is a form of mechanical energy that has the 'potential' to be converted into other forms of energy, such as kinetic energy. This calculator addresses the two most common types: gravitational and elastic potential energy.
Gravitational Potential Energy (GPE)
GPE is the energy an object has because of its vertical position in a gravitational field. The higher an object is lifted against gravity, the more gravitational potential energy it stores. The formula is U = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height.
Elastic Potential Energy (EPE)
EPE is the energy stored in an elastic object, like a spring or a rubber band, when it is stretched or compressed. This energy is a result of the deformation of the object from its equilibrium position. The formula is U = 1/2 k x^2, where 'k' is the spring constant and 'x' is the displacement from equilibrium.

Step-by-Step Guide to Using the Potential Energy Calculator

  • Selecting the Energy Type
  • Inputting Values for GPE
  • Inputting Values for EPE
1. Choose Your Calculation
Start by selecting either 'Gravitational' or 'Elastic' from the energy type dropdown menu. This will display the relevant input fields for your calculation.
2. For Gravitational Potential Energy
You will need to provide the object's Mass (in kg), its Height (in meters) relative to a reference point, and the local acceleration due to Gravity (in m/s²). The calculator defaults to Earth's gravity (9.81 m/s²), but you can adjust this for calculations on other planets or in different scenarios.
3. For Elastic Potential Energy
You need the Spring Constant (k) of the object in Newtons per meter (N/m) and the Displacement (x) from its equilibrium (resting) position in meters. Displacement can be either compression or stretching.
4. Calculate and Interpret
After entering the values, click the 'Calculate' button. The result will be displayed in Joules (J), the standard unit of energy.

Real-World Applications of Potential Energy

  • Hydroelectric Power
  • Roller Coasters and Amusement Park Rides
  • Mechanical Devices
Hydroelectric Dams
Dams store vast amounts of water at a significant height. This stored gravitational potential energy is converted into kinetic energy as the water flows down, which then turns turbines to generate electricity.
Roller Coasters
A roller coaster car is pulled to the top of the first hill, giving it a large amount of gravitational potential energy. This energy is then converted into kinetic energy as it descends, powering it through the rest of the track.
Springs, Shock Absorbers, and Archery
Elastic potential energy is fundamental to many mechanical systems. Car shock absorbers use springs to dampen bumps. An archer stores elastic potential energy in the bowstring, which is then transferred to the arrow as kinetic energy upon release.

Common Misconceptions and Correct Methods

  • The Role of the Reference Point (h=0)
  • Energy is Not 'Lost'
  • Understanding the Spring Constant
The Zero-Height Reference Point is Arbitrary
Gravitational potential energy is a relative value. It depends on the 'zero level' you choose. For example, a book on a table has potential energy relative to the floor, but zero potential energy relative to the table itself. What matters for calculations is the change in height (Δh).
Energy Conservation vs. 'Losing' Energy
In a closed system, energy is conserved, not lost. It transforms from one form to another (e.g., potential to kinetic). However, in real-world systems, some energy is often 'lost' to non-conservative forces like friction and air resistance, where it is converted into heat.
What the Spring Constant (k) Really Means
The spring constant 'k' is a measure of stiffness. A high 'k' value means the spring is very stiff and requires a lot of force to stretch or compress. A low 'k' value indicates a softer, more flexible spring.

Mathematical Derivation and Examples

  • Deriving the GPE Formula
  • Deriving the EPE Formula
  • Worked-Out Examples
Gravitational Potential Energy (GPE)
The work (W) done to lift an object against gravity is W = Force × distance. The force required is equal to the object's weight (mg). The distance is the height (h). Therefore, W = mg × h. By the work-energy theorem, the work done on the object is equal to the potential energy it gains. Thus, U_g = mgh.
Elastic Potential Energy (EPE)
According to Hooke's Law, the force required to stretch or compress a spring is F = kx. However, this force is not constant; it increases with displacement. To find the work done (and thus the stored energy), we must integrate the force over the displacement: W = ∫F dx = ∫kx dx. The result of this integral from 0 to x is (1/2)kx². Thus, U_e = (1/2)kx².

Calculation Examples

  • GPE Example: What is the potential energy of a 5 kg bowling ball held at a height of 2 meters? U = 5 kg * 9.81 m/s² * 2 m = 98.1 Joules.
  • EPE Example: A spring with k = 300 N/m is compressed by 10 cm (0.1 m). What is its potential energy? U = 0.5 * 300 N/m * (0.1 m)² = 1.5 Joules.