Elastic Potential Energy Calculator

Elastic potential energy stored in a spring is: E = ½ · k · x²

• E = elastic potential energy
• k = spring constant (stiffness)
• x = displacement from equilibrium (stretch or compression)

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This tool assumes linear behavior (Hooke’s law region). If the spring is overstretched, real energy may differ.

1. Select what you want to solve for: E, k, or x.
2. Enter the other two values and choose units for each.
3. Pick decimal places for rounding.
4. Enable “Show calculation steps” if you want the math displayed.
5. Press Calculate, then export with CSV or PDF.

1) Typical spring constant values

Small classroom springs often measure 50–500 N/m, while bench springs can be 800–2500 N/m. If you know force and stretch, estimate k using k = F/x; 20 N at 0.05 m implies about 400 N/m.

2) Displacement measurement tips

Measure x from the unloaded length to the stretched or compressed length. A 1 cm error at x = 5 cm changes x by 20%, and energy by about 44% because E scales with x². Record three trials and average, such as 0.048 m, 0.050 m, 0.052 m → mean 0.050 m.

3) Energy growth with stretch

Doubling displacement quadruples energy. With k = 300 N/m, x = 0.10 m gives E = 1.50 J, but x = 0.20 m gives E = 6.00 J. This steep growth explains why small extra stretch raises stored energy rapidly.

4) Reverse solving checks

When solving for k or x, plug the result back in. If E = 9 J and x = 0.15 m, you get k ≈ 800 N/m; 0.5 × 800 × 0.15² = 9.0 J. If rounding hides agreement, increase decimals to 6–8.

5) Unit conversion reference

Internally, the calculator uses base units (N/m, m, J). Conversions: 1 in = 0.0254 m, 1 ft = 0.3048 m, and 1 ft·lbf ≈ 1.35582 J. Also, 1 lbf/in ≈ 175.127 N/m, so 30 lbf/in ≈ 5253.8 N/m.

6) Linear-region reminder

The formula assumes a linear spring. If a safe travel is 40 mm, staying under 30–35 mm helps avoid permanent set. For rubber bands, stiffness changes with stretch, so treat results as an estimate and measure force at multiple x values.

7) Recording results for reports

Use CSV export to capture inputs, units, and base-unit values. In lab reports, include k, x, and E plus uncertainty. Example: k = 400 ± 10 N/m and x = 0.050 ± 0.002 m gives E ≈ 0.50 J, with uncertainty dominated by the x² term. Switch units first, then calculate to reduce copy mistakes during reporting later.

1) What is elastic potential energy?

It is stored energy in a stretched or compressed elastic element. For an ideal spring, it equals E = ½·k·x², where k is stiffness and x is displacement from equilibrium.

2) Can I use compression instead of stretch?

Yes. Use the magnitude of compression as x. The energy depends on x², so stretch and compression of the same size store the same energy in an ideal linear spring.

3) How can I determine the spring constant k?

Measure force and displacement in the linear region. Compute k = F/x, using consistent units. Example: 10 N at 0.04 m gives k = 250 N/m.

4) Why does energy rise quickly with displacement?

Because energy is proportional to x². If you double x, energy becomes four times larger. This is why small measurement errors in x can noticeably change E.

5) What if my spring or band is not linear?

Then k changes with displacement and the simple formula becomes approximate. For better accuracy, measure force at several x values and integrate the force–displacement curve, or use the average k only over the tested range.

6) Which units are best for accurate results?

Choose units you can measure reliably, then convert. Many labs use N/m and meters. For imperial measurements, lbf/in and inches work, and the calculator converts to base units for consistent computation.