Hooke’s Law Calculator

Compute spring force, extension, and stiffness instantly today. Switch units, visualize curves, export results easily. Perfect for labs, homework, design checks, and simulations anywhere.

Meta description: Accurately solve Hooke’s law problems for springs and elastic materials quickly. Get force, extension, k, energy, and stress with unit tools fast results.

Calculator

Pick spring or material form.
Enter the other required fields.
0–50, for range estimates.
Energy uses U = ½kx².
Strain is dimensionless.
Required fields depend on “Solve for”.

Example data

Mode Given Computed
Spring (F = kx) k = 250 N/m, x = 0.08 m F = 20 N, U = 0.8 J
Spring (F = kx) F = 30 N, x = 0.06 m k = 500 N/m, U = 0.9 J
Material (σ = Eε) E = 200 GPa, ε = 0.001 σ = 200 MPa
Material (σ = Eε) σ = 120 MPa, E = 70 GPa ε ≈ 0.001714

These are typical elastic-region examples; real materials may deviate outside linear ranges.

Formula used

  • Spring form: F = kx, where F is force, k is spring constant, and x is extension.
  • Elastic energy: U = ½kx², stored as the spring stretches or compresses.
  • Material form: σ = Eε, where σ is stress, E is Young’s modulus, and ε is strain.

How to use

  1. Choose Mode: Spring or Material.
  2. Select Solve for to decide the unknown variable.
  3. Enter the other required values and pick units.
  4. Optionally set Tolerance (%) to see an output range.
  5. Press Calculate; results appear above this form.
  6. Use Download CSV or Download PDF to export.

Article

Linear elastic behavior in everyday components

Hooke’s law models how many springs, clips, and compliant parts respond to small loads. Within the elastic region, deformation is proportional to the applied load, so a single constant summarizes stiffness. This calculator lets you work in spring form for devices and in material form for stress–strain checks.

Spring mode outputs for lab measurements

In spring mode, enter any two of force, extension, and spring constant. The tool converts common units, solves F = kx, and reports elastic energy using U = ½kx². For example, k = 250 N/m and x = 0.08 m gives F = 20 N and U = 0.8 J, matching typical bench experiments.

Material mode for quick stress–strain estimates

In material mode, the relationship σ = Eε helps estimate stress from strain gauges, or strain from a measured stress and modulus. Using E = 200 GPa and ε = 0.001 yields σ = 200 MPa. Because strain is dimensionless, accuracy depends mainly on consistent stress units and a modulus appropriate to temperature and alloy.

Reading the Plotly curve for insight

The interactive plot shows the linear curve implied by your inputs. For springs it graphs force versus extension and highlights your calculated point, revealing how doubling extension doubles force. For materials it plots stress versus strain and marks your operating point. This visual check helps spot unit mistakes and unrealistic magnitudes immediately.

Using tolerance to bracket uncertainty

Real measurements carry uncertainty from sensors and rounding. The tolerance field provides a practical range by applying a percentage bound to the relevant product or ratio. If you set 5%, the calculator estimates a minimum and maximum for the solved quantity. Use this to report results with sensible significant figures.

Engineering notes and responsible use

Hooke’s law applies only while behavior remains linear and reversible. Springs can yield, buckle, or reach coil bind; materials can plastically deform or creep. When loads are large, geometry changes, or the curve is nonlinear, treat these results as preliminary screening and validate with specifications, testing, or a fuller constitutive model. For design, compare computed stress to allowable values and safety factors, and compare spring energy to impact requirements; record units in reports, and rerun with measured k from calibration curves when conditions change.

FAQs

Does Hooke’s law work for large deformations?

No. It is reliable only in the linear elastic region. Beyond that, stiffness can change, coils may bind, and materials may yield or creep, so proportionality breaks down.

What is the difference between spring constant and Young’s modulus?

Spring constant describes a specific device’s stiffness, including geometry. Young’s modulus is a material property relating stress to strain. Device stiffness depends on both modulus and shape.

Why does the calculator show elastic energy?

Elastic energy quantifies stored work in a stretched or compressed spring. It is useful for impact, vibration, and return-force problems where energy, not only force, matters.

How should I choose units to avoid mistakes?

Pick units that match your measurement instruments, then keep them consistent. Use the plot as a sanity check: slopes and magnitudes should look realistic for your system.

What does the tolerance range represent?

It is a practical bracket based on a percentage bound applied to the relevant inputs. It is not a statistical confidence interval, but it helps communicate plausible variation.

Can I use this for compression as well as extension?

Yes. Use negative extension or force to represent compression, depending on your sign convention. The linear relationship remains the same while the system stays elastic.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.