Energy stored in a spring
What is elastic potential energy?
Elastic potential energy is stored when an elastic object, such as a spring, is stretched or compressed from its equilibrium position.
Formula
Elastic potential energy formula
Elastic EnergyE = ½kx²
- E is elastic potential energy in joules.
- k is the spring constant in newtons per meter.
- x is extension or compression in meters.
Worked example
A 200 N/m spring extends 0.5 m
- Write the formula: E = ½kx².
- Substitute the values: E = ½ × 200 × 0.5².
- Calculate the energy: E = 25 J.
Rearranged equations
Solve for spring constant or extension
Spring Constant
k = 2E ÷ x²
Multiply energy by two, then divide by the square of extension.
Extension
x = √(2E ÷ k)
Divide twice the energy by the spring constant, then take the square root.
Units
Standard SI units
Use newtons per meter for spring constant and meters for extension.
Spring constantk in N/m
Hooke's law region
When does this formula apply?
The formula assumes the spring behaves elastically and remains within the region where its spring constant is effectively constant.
Calculation limits
Important assumptions
- Spring constant must be greater than zero.
- Extension magnitude must be greater than zero.
- Elastic energy must be greater than zero when solving for another variable.
- The spring is assumed to remain in its elastic range.
- The calculator does not automatically convert units.
Related tools
Continue analyzing energy
Use the Gravitational Potential Energy Calculator to calculate energy due to height.
Use the Kinetic Energy Calculator for motion energy, or use the Work Calculator for force and displacement.
Questions and answers
Elastic potential energy FAQ
What formula does the elastic potential energy calculator use?
It uses E = ½kx², where elastic potential energy equals one-half multiplied by the spring constant and the square of the extension.
What is the SI unit of elastic potential energy?
The SI unit is the joule, written as J.
What is the unit of spring constant?
The SI unit of spring constant is newtons per meter, written as N/m.
Can the extension be zero or negative?
This calculator requires a positive extension magnitude when performing the calculation.