Spring force tool

Hooke's Law Calculator

Solve force, spring constant, or extension using F = kx.

Enter two known values

Solve a Hooke's law problem

Free tool
N

This is the value being calculated.

N/m

Positive stiffness of the spring.

m

Positive extension or compression from equilibrium.

Use newtons for force, newtons per meter for spring constant, and meters for extension.

Try an example:

Your Hooke's law result will appear here

Choose the missing variable and enter the other two known values.

Calculator guide

How this calculator works

Hooke's Law Calculator determines the relationship between force, spring constant, and displacement in elastic systems. It helps physics students, engineers, and laboratory users analyze springs, mechanical components, and material elasticity using force-extension relationships.

Formula explanation

Hooke's law describes the relationship between applied force and spring displacement using F = kx.

Formula

Spring Force = Spring Constant × Displacement

Worked example

Example: A stronger spring requires more force for the same displacement.

Assumptions

  • The spring follows ideal Hooke's law behavior.
  • The spring remains within its elastic limit.
  • Spring constant remains constant during calculation.
  • Input values use compatible scientific units.

Examples

  • Example: Calculate spring force when spring constant and displacement are known.
  • Example: Engineers test mechanical springs by measuring force and extension relationships.

Common mistakes

  • Using incorrect spring constants.
  • Ignoring displacement direction.
  • Applying the law beyond elastic limits.

Variables

  • Applied spring force
  • Spring constant
  • Extension or compression distance
  • Elastic displacement
  • Material stiffness
  • Measurement units

Limitations

  • Results assume ideal elastic spring behavior.
  • Nonlinear materials require advanced mechanical analysis methods.

Scientific references

  • OpenStax University Physics: Elasticity and Hooke's Law
  • NIST SI force measurement references
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Mechanical engineering design
  • Spring system analysis
  • Material elasticity studies
  • Laboratory force experiments
  • Mechanical component testing

Frequently asked questions

How is Hooke's law calculated?

Hooke's law is calculated using F = kx, where force equals the spring constant multiplied by displacement.

What does the spring constant represent?

The spring constant represents spring stiffness and shows how much force is required to produce a specific displacement.

When does Hooke's law not apply?

Hooke's law does not apply when a spring exceeds its elastic limit and experiences permanent deformation.

What factors affect spring force?

Spring force depends on the spring constant and the amount of stretching or compression from the equilibrium position.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

Spring deformation

What is Hooke's law?

Hooke's law describes the relationship between the force applied to a spring and the spring's extension or compression.

Formula

Hooke's law formula

Spring ForceF = kx

  • F is force in newtons.
  • k is spring constant in newtons per meter.
  • x is extension or compression in meters.

Worked example

A 200 N/m spring extends 0.3 m

  1. Write the formula: F = kx.
  2. Substitute the values: F = 200 × 0.3.
  3. Calculate the force: F = 60 N.

Rearranged equations

Solve for spring constant or extension

Spring Constant

k = F ÷ x

Divide force by extension.

Extension

x = F ÷ k

Divide force by spring constant.

Units

Standard SI units

Use newtons for force, newtons per meter for spring constant, and meters for extension.

Elastic behavior

The elastic limit

Hooke's law is valid only while the spring returns to its original shape after the force is removed. Beyond the elastic limit, force and extension may no longer be proportional.

Calculation limits

Important assumptions

  • Spring constant must be greater than zero.
  • Extension magnitude must be greater than zero.
  • Force must be greater than zero when solving for another variable.
  • The spring is assumed to remain within its elastic region.
  • The calculator does not automatically convert units.

Related tools

Use the Elastic Potential Energy Calculator to calculate energy stored in a spring.

Use the Force Calculator for force, mass, and acceleration.

Questions and answers

Calculator FAQ

How is Hooke's law calculated?

Hooke's law is calculated using F = kx, where force equals the spring constant multiplied by displacement.

What does the spring constant represent?

The spring constant represents spring stiffness and shows how much force is required to produce a specific displacement.

When does Hooke's law not apply?

Hooke's law does not apply when a spring exceeds its elastic limit and experiences permanent deformation.

What factors affect spring force?

Spring force depends on the spring constant and the amount of stretching or compression from the equilibrium position.