🔧 Elastic Potential Energy Calculator
Calculate spring potential energy
How to Use This Calculator
Enter Spring Constant
Input the spring constant (k) in Newtons per meter (N/m). This measures the stiffness of the spring. Higher values indicate stiffer springs. Typical values range from 10-1000 N/m for common springs.
Enter Displacement
Enter the displacement (x) in meters. This is how far the spring is stretched or compressed from its equilibrium position. Compression uses negative values, but the calculator uses the absolute value.
Calculate Energy
Click the "Calculate" button to compute the elastic potential energy stored in the spring. The calculator also shows the restoring force the spring exerts.
Review Results
Review the calculated elastic potential energy in Joules and the restoring force in Newtons. These values help understand the spring's energy storage capacity.
About Elastic Potential Energy Calculator
The Elastic Potential Energy Calculator computes the energy stored in a spring when it is stretched or compressed. This energy is based on Hooke's Law and represents the work done to deform the spring. The calculator also provides the restoring force, which is the force the spring exerts to return to its equilibrium position.
When to Use This Calculator
- Physics Problems: Solve homework problems involving spring energy
- Engineering Design: Calculate energy storage in spring-based systems
- Mechanical Systems: Design shock absorbers, suspension systems, and vibration dampers
- Energy Storage: Evaluate spring-based energy storage devices
- Educational Purposes: Understand Hooke's Law and elastic potential energy
Why Use Our Calculator?
- ✅ Dual Output: Provides both potential energy and restoring force
- ✅ Step-by-Step Formula: Shows the calculation process
- ✅ Accurate Calculations: Uses standard physics formulas
- ✅ Instant Results: Get answers immediately
- ✅ Free to Use: No registration or payment required
Understanding Elastic Potential Energy
Elastic potential energy is the energy stored in elastic materials when they are deformed. For springs, this energy depends on the spring constant (stiffness) and the square of the displacement. When you compress or stretch a spring, you're doing work against the spring's restoring force, and that work is stored as potential energy. When released, this energy is converted to kinetic energy.
Formula
PE = ½kx²
F = -kx (restoring force)
Where:
- PE = Elastic Potential Energy (Joules)
- k = Spring Constant (N/m)
- x = Displacement from equilibrium (meters)
- F = Restoring Force (Newtons, negative sign indicates direction)
Example Calculation:
For a spring with k = 100 N/m and x = 0.1 m:
PE = ½ × 100 × (0.1)²
PE = 0.5 × 100 × 0.01
PE = 0.5 J
F = -100 × 0.1 = -10 N (force opposes displacement)
Frequently Asked Questions
What is elastic potential energy?
Elastic potential energy is the energy stored in elastic materials (like springs) when they are deformed from their equilibrium position. It's based on Hooke's Law and represents the work done to compress or stretch the material. This energy can be released when the material returns to its original shape.
What is the spring constant and how do I find it?
The spring constant (k) measures a spring's stiffness—how much force is needed to stretch or compress it by a unit distance. It's measured in N/m. You can find it by dividing the force applied by the displacement: k = F/x. It's often provided in spring specifications or can be measured experimentally.
Why is displacement squared in the energy formula?
The displacement is squared because energy is the integral of force over distance. Since force is proportional to displacement (F = kx), the work done (energy) is proportional to x². This means doubling the displacement quadruples the stored energy, which is why springs store more energy when stretched further.
Does it matter if the spring is compressed or stretched?
For the energy calculation, it doesn't matter—the formula uses the absolute value of displacement. However, the restoring force has opposite directions: compression produces a force pushing outward, while stretching produces a force pulling inward. The negative sign in F = -kx indicates the force opposes the displacement.
What are typical spring constant values?
Spring constants vary widely: small springs (like in pens) might be 10-100 N/m, medium springs (car suspension) 10,000-50,000 N/m, and very stiff springs can exceed 100,000 N/m. The value depends on the spring material, coil diameter, wire diameter, and number of coils. Stiffer springs require more force to deform.