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.
| 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.