Potential Energy Calculator

About Potential Energy Calculator

The Potential Energy Calculator computes the energy stored in an object due to its position or configuration. It supports two fundamental types: gravitational potential energy (PE = mgh) for objects at a height, and elastic potential energy (PE = ½kx²) for compressed or stretched springs. Enter any two known values to solve for the third, with detailed step-by-step solutions, real-world comparisons, and multi-unit support.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. The higher the object, the more potential energy it stores.

Where m is mass (kg), g is gravitational acceleration (m/s²), and h is height above the reference point (m).

Elastic Potential Energy

Elastic potential energy is the energy stored in a spring or elastic material when it is stretched or compressed from its equilibrium position. This follows Hooke’s Law, where the restoring force is proportional to displacement.

Where k is the spring constant (N/m) and x is the displacement from equilibrium (m).

How to Use This Calculator

1. Choose the energy type: Select the Gravitational tab for objects at a height (PE = mgh) or the Elastic tab for springs and elastic materials (PE = ½kx²).
2. Enter known values with units: For gravitational PE, enter mass, height, and select a planet. For elastic PE, enter the spring constant and displacement. Leave the unknown field blank.
3. Click Calculate: The calculator determines which formula rearrangement to use automatically.
4. Review the detailed solution: Examine the step-by-step solution, real-world energy comparisons, impact velocity insights, and the energy unit conversion table.

Gravity on Different Celestial Bodies

Conservation of Energy

One of the most powerful principles in physics is the conservation of mechanical energy. When only conservative forces act (like gravity), the total mechanical energy remains constant:

PE + KE = constant

For a falling object: as height decreases, gravitational PE converts to kinetic energy. At the ground, all PE has become KE, giving an impact velocity of v = √(2gh). For a released spring: elastic PE converts entirely to kinetic energy of the attached mass, giving v = √(2PE/m).

Real-World Applications

Hydroelectric Power

Dams store gravitational PE in elevated water. When released through turbines, this PE converts to kinetic energy and then electrical energy. A reservoir 100 m high with 1 million kg of water stores about 981 MJ of potential energy.

Roller Coasters

The initial climb stores gravitational PE, which powers the entire ride. Designers calculate the maximum height to ensure enough energy for all loops and turns, accounting for friction losses.

Springs and Mechanisms

Elastic PE powers mechanical watches, vehicle suspensions absorb road bumps, and archery bows store energy in their limbs to propel arrows. The spring constant determines how stiff the spring is and how much energy it can store.

Frequently Asked Questions

What is potential energy?

Potential energy is stored energy that an object possesses due to its position, configuration, or condition. The two most common types are gravitational potential energy (PE = mgh), which depends on an object’s height above a reference point, and elastic potential energy (PE = ½kx²), which is stored in a stretched or compressed spring.

What is the formula for gravitational potential energy?

The gravitational potential energy formula is PE = mgh, where PE is potential energy in joules, m is mass in kilograms, g is gravitational acceleration (9.807 m/s² on Earth), and h is height above the reference point in meters. This can be rearranged to solve for mass (m = PE/gh) or height (h = PE/mg).

What is elastic potential energy?

Elastic potential energy is the energy stored in an elastic object, such as a spring, when it is stretched or compressed from its natural length. The formula is PE = ½kx², where k is the spring constant in newtons per meter and x is the displacement from equilibrium in meters. This follows Hooke’s law.

How does potential energy convert to kinetic energy?

When an object falls from a height, its gravitational potential energy converts to kinetic energy. By conservation of energy (ignoring friction), PE = KE, so mgh = ½mv², giving v = √(2gh). Similarly, when a compressed spring is released, elastic PE converts to kinetic energy of the attached object.

Does gravity vary on different planets?

Yes, gravitational acceleration varies significantly across celestial bodies. Earth has g = 9.807 m/s², while the Moon has only 1.625 m/s² (about 1/6 of Earth). Jupiter has the strongest gravity among planets at 24.79 m/s². This means the same object at the same height has different potential energy on different planets.

Additional Resources

• Potential Energy - Wikipedia
• Hooke’s Law - Wikipedia
• Conservation of Energy - Wikipedia

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