Elastic Potential Energy Calculator

What is Elastic Potential Energy?

Elastic potential energy is the energy stored in an elastic material or spring when it is stretched or compressed. When you pull a spring, work is done against the restoring force, and this work gets stored as potential energy. The formula for elastic potential energy is U = ½kΔx², where U is the elastic energy in joules, k is the spring constant in newtons per meter, and Δx is the displacement from the equilibrium position in meters.

How to Use This Calculator

Choose which variable you want to solve for: elastic energy (U), spring constant (k), or displacement (Δx). Enter the known values in any supported units, and the calculator will instantly compute the result with step-by-step solutions. The calculator supports multiple units for energy (joules, kilojoules, BTU, calories, watt-hours, electronvolts), spring constant (N/m, N/mm, lb/ft, lb/in), and displacement (meters, centimeters, millimeters, inches, feet).

Elastic Potential Energy Formula

The fundamental equation used is:

U = ½ × k × Δx²

Derived Formulas

To find spring constant: k = 2U / Δx²

To find displacement: Δx = √(2U / k)

Example Calculation

If a spring has a spring constant of 200 N/m and is stretched by 0.3 meters, the elastic potential energy stored is:

U = ½ × 200 × (0.3)²

U = ½ × 200 × 0.09

U = 9 joules

Frequently Asked Questions

What is the spring constant?

The spring constant (k) is a measure of a spring's stiffness. It represents the force required to stretch or compress a spring by one unit of length. A higher spring constant means a stiffer spring that requires more force to deform.

What units does this calculator support?

The calculator supports multiple units for energy (joules, kilojoules, megajoules, BTU, calories, kilocalories, watt-hours, kilowatt-hours, electronvolts, foot-pounds), spring constant (N/m, N/mm, lb/ft, lb/in, gf/m, kgf/m), and displacement (meters, centimeters, millimeters, kilometers, inches, feet, miles). All conversions are handled automatically.

What is Hooke's Law?

Hooke's Law states that the force needed to extend or compress a spring by some distance is proportional to that distance: F = -kΔx. Elastic potential energy is derived from this law by integrating the force over the displacement, giving U = ½kΔx².

Can displacement be negative?

Displacement can be positive or negative depending on the direction (stretching vs. compression), but since the formula uses Δx², the elastic potential energy is always positive regardless of direction. The calculator accepts positive values for displacement magnitude.

What are real-world applications of elastic potential energy?

Elastic potential energy has many practical applications including suspension systems in vehicles, trampolines, bow and arrow mechanisms, pogo sticks, mechanical watches, and shock absorbers. It is also fundamental in engineering design for springs and elastic components.

Report