Hooke's Law states that the force needed to extend or compress a spring is proportional to the distance it is displaced: F = k * x. Here, F is the restoring force (N), k is the spring constant (N/m), and x is the displacement from the natural length (m). The law holds within the elastic limit of the material.

What does the spring constant k represent?

The spring constant k (measured in N/m) describes the stiffness of a spring. A high k means a stiff spring that requires more force to stretch or compress. A low k means a soft spring that deforms easily under small forces.

What is the elastic potential energy formula?

Elastic potential energy (PE) is the energy stored in a spring when it is deformed: PE = 0.5 * k * x². It is measured in Joules (J). When the spring is released, this energy converts to kinetic energy.

When does Hooke's Law break down?

Hooke's Law is only valid within the elastic limit of the spring material. Beyond this limit, the spring deforms permanently (plastic deformation) and the linear relationship between force and displacement no longer holds.

Can the displacement be negative?

Yes. Displacement can be negative to indicate compression (spring is shorter than natural length) vs. positive for extension. However, the magnitude of force and elastic potential energy depend on the absolute value of x, so this calculator uses positive displacement values.

What are typical spring constant values?

Spring constants vary enormously: small pen springs ~200–500 N/m, door springs ~1,000–5,000 N/m, car suspension coil springs ~15,000–50,000 N/m, and stiff industrial springs can exceed 1,000,000 N/m.

Hooke's Law Calculator

Solve for force, spring constant, or displacement using Hooke's Law (F = k * x) — plus see the elastic potential energy stored in the spring.

Inputs

Select the variable to solve for, then enter the other two known values.

Solve For

Spring Constant (k)

Displacement (x)

Force (F)

Result

Fill in the inputs and press Calculate.

Formula Reference

F = k × x — restoring force (N)

k = F / x — spring constant (N/m)

x = F / k — displacement (m)

PE = ½ k x² — elastic potential energy (J)

Summary

Hooke's Law states that the restoring force exerted by a spring is directly proportional to the displacement from its natural length: F = k * x. This calculator lets you solve for any one of the three variables — force (F), spring constant (k), or displacement (x) — given the other two. It also computes the elastic potential energy (PE = 0.5 * k * x²) stored in the spring at that displacement. Both SI and imperial units are supported.

How it works

Choose the variable you want to calculate: Force (F), Spring Constant (k), or Displacement (x).
Enter known values for the other two variables in the input fields.
Select the appropriate units for each quantity.
Click Calculate to see the result, full working, and the elastic potential energy stored in the spring.
Use Reset to clear all fields and start a new calculation.

Use cases

Find the force a spring exerts when stretched or compressed by a known amount.
Determine the spring constant (stiffness) from a measured force and displacement.
Calculate how far a spring will extend under a given load.
Compute elastic potential energy stored in springs for mechanical design.
Verify experimental lab results in physics or engineering courses.
Analyze suspension, valve, or actuator springs in mechanical systems.
Understand spring behavior for prototyping elastic or flexible structures.
Cross-check spring specifications when selecting components for a design.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu