Elastic Potential Energy Calculator
U = ½kΔx²
Answer
Tracking spring energy by hand means juggling stiffness in N/m, stretch in inches, and answers in joules—all on the same scratchpad. One unit slip and your stored-energy figure is off. This page lets you pick what you are solving for, enter values in the units you actually measured, and get the missing variable without redoing the algebra.
How to Use This Elastic Potential Energy Calculator
- Choose a calculation. Use the dropdown to solve for elastic energy U, spring constant k, or displacement Δx. The field marked (calculated) clears and locks while you enter the other two values.
- Enter your known values. Type positive numbers in the unlocked fields. Pick energy, stiffness, and length units from each row’s dropdown—mixed units on one run are fine; the tool converts internally before applying the formula.
- Set significant figures. Leave auto for full precision, or choose 3–9 sig figs to match a lab worksheet or textbook problem.
- Press Calculate. The answer appears in the result panel and in the calculated field.
Elastic Potential Energy Formulas and Practical Applications
Think of a garage-door spring or a physics-lab coil: the farther you stretch or compress it from rest, the more energy it stores—like pulling back a slingshot band. That stored amount is elastic potential energy.
U = ½kΔx²
U is energy in joules (by default), k is spring stiffness (how hard the spring pushes back per meter of stretch), and Δx is displacement from the equilibrium position—not total length, just the change from neutral.
In our testing, a spring with k = 200 N/m stretched Δx = 0.15 m stores U = 2.25 J—half of 200 × 0.15². Need stiffness instead? Rearrange to k = 2U / Δx². Need displacement? Use Δx = √(2U / k).
Common jobs this formula covers
- Estimating energy in a compressed coil before release (launchers, bumpers, shock mounts).
- Back-solving spring constant from a measured stretch and known energy input.
- Homework and lab reports where two variables are given and the third must be found.
Standard Units and Conversion Tables
Elastic energy units
| Unit | Symbol | Notes |
|---|---|---|
| Joule | J | SI default; 1 J = 1 N·m |
| Kilojoule | kJ | 1 kJ = 1,000 J |
| Megajoule | MJ | 1 MJ = 10⁶ J |
| Calorie | cal | 1 cal ≈ 4.184 J |
| Foot-pound force | ft·lbf | Common in US mechanical specs |
Spring constant units
| Unit | Typical use |
|---|---|
| N/m | SI default for physics and engineering |
| N/mm | Stiff springs quoted per millimeter |
| lb/in, lb/ft | US hardware and automotive catalogs |
| kgf/m, gf/m | Metric gravitational force per meter |
Displacement units
Meters, centimeters, kilometers, inches, feet, and miles are supported. Enter how far the spring moved from equilibrium—not its total physical length.
Frequently Asked Questions
What is elastic potential energy?
Elastic potential energy is the work stored when a spring (or similar elastic body) is stretched or compressed from its relaxed shape. Release that deformation and the energy can become motion or heat.
Which variable can this calculator solve for?
Pick Calculate U, Calculate k, or Calculate Δx from the dropdown. Enter the other two known values and press Calculate.
What units of energy does the calculator accept?
J, kJ, MJ, BTU, cal, kcal, W·h, kW·h, eV, and ft·lbf. Spring constants and displacements have their own unit lists on each input row.
Why does displacement get squared in the spring energy formula?
Force from Hooke’s law rises linearly with stretch, but energy is force integrated over distance, so stored energy scales with Δx². That is why doubling stretch quadruples U.
Working with Newton’s second law next? Try the Force Calculator. For mass–energy equivalence, see the E = mc² Calculator. Browse all physics calculators on RapidRatio.