Is potential energy always positive?

Gravitational PE can be negative if the object is below the chosen reference point. The reference height (where PE = 0) is arbitrary. In orbital mechanics, PE is conventionally negative, reaching zero at infinite distance.

Where does potential energy come from?

Potential energy is stored by doing work against a force. Lifting a book against gravity stores gravitational PE. Compressing a spring against its restoring force stores elastic PE. The energy comes from whatever does the lifting or compressing.

How is potential energy used in power generation?

Hydroelectric plants convert gravitational PE of water into electricity. Pumped-storage facilities pump water uphill when electricity is cheap and release it through turbines during peak demand, effectively using PE as a battery.

What is elastic potential energy?

Elastic PE is energy stored in a deformed elastic object like a spring, rubber band, or bow. It equals 0.5 × k × x^2, where k is the spring constant and x is the deformation from equilibrium.

Does potential energy depend on the path taken?

No. Gravitational potential energy depends only on the starting and ending heights, not the path between them. This makes gravity a conservative force. The PE of a book on a shelf is the same whether you lifted it straight up or carried it up a winding staircase.

Potential Energy Calculator

PE = m × g × h

Potential Energy

Gravitational potential energy

Mass (kg)

Height (m)

Formula

PE = m × g × h (g = 9.81 m/s²)

What Is Potential Energy?

Potential energy is the stored energy an object has due to its position, configuration, or state. It is energy that has the potential to be converted into other forms — most commonly kinetic energy. The two most common types are gravitational potential energy (GPE) and elastic potential energy (EPE).

Gravitational potential energy depends on an object's mass, height above a reference point, and gravitational acceleration. Elastic potential energy is stored in stretched or compressed springs and elastic materials. Both types are scalar quantities measured in joules (J) and are fundamental to understanding energy conservation in physical systems.

How to Use the Potential Energy Calculator

Select the type: gravitational (mass + height) or elastic (spring constant + displacement).
For gravitational PE: enter mass (kg) and height (m) above your reference point.
For elastic PE: enter spring constant k (N/m) and displacement x (m) from equilibrium.
Click Calculate to get the potential energy in joules (J).

Formula & Explanation

Gravitational PE:
  GPE = m × g × h

Elastic PE:
  EPE = ½ × k × x²

m = mass (kg)
g = 9.81 m/s² (Earth surface)
h = height above reference (m)
k = spring constant (N/m)
x = displacement from equilibrium (m)

GPE is defined relative to a chosen reference height. Only differences in GPE matter physically — the choice of reference point is arbitrary.

Worked Examples

Book on a Shelf

A 2 kg book is placed on a shelf 1.5 m above the floor. GPE = 2 × 9.81 × 1.5 = 29.43 J. If knocked off, it will have 29.43 J of kinetic energy just before hitting the floor (ignoring air resistance), reaching a speed of √(2 × 29.43 / 2) = 5.42 m/s.

Compressed Spring

A spring with k = 800 N/m is compressed by 0.05 m (5 cm). EPE = ½ × 800 × 0.05² = ½ × 800 × 0.0025 = 1.0 J. When released, this energy converts to kinetic energy of the projectile or mechanism it drives.

Hydroelectric Dam

Water in a reservoir 50 m above the turbines: 1000 kg of water has GPE = 1000 × 9.81 × 50 = 490,500 J = 490.5 kJ. A 200 MW dam drops ~400,000 kg of water per second through its turbines, releasing enormous gravitational PE as electricity.

Frequently Asked Questions

What is the conservation of energy?▾

The law of conservation of energy states that energy cannot be created or destroyed — only converted from one form to another. When an object falls, GPE converts to KE. When a spring is compressed, KE converts to EPE. In a closed system the total mechanical energy (KE + PE) remains constant.

Why is potential energy defined relative to a reference point?▾

Only changes in potential energy are physically meaningful. A book 1 m above a table and 2 m above the floor has different PE values depending on your reference, but the energy released when it falls to any given surface is the same. Physicists choose whichever reference point makes calculation easiest.

What is zero potential energy?▾

Zero PE is set at whatever reference point you choose. Common choices: Earth's surface (h = 0), the ground under a system, or infinity for planetary calculations. For gravity at large distances, PE → 0 as r → ∞ (PE = −GMm/r convention).

How is elastic potential energy used in engineering?▾

Springs and elastic materials store EPE in countless applications: vehicle suspensions absorb road shocks; archery bows store draw energy; clock mainsprings power mechanisms; pogo sticks and trampolines bounce using EPE. The EPE = ½kx² formula lets engineers size springs for required energy storage.

What is chemical potential energy?▾

Chemical PE is stored in the bonds between atoms. When fuel burns, chemical bonds break and reform, releasing energy as heat and light. A liter of gasoline contains ~31.5 MJ of chemical PE. Batteries store chemical PE and release it as electrical energy.