Hooke's Law Calculator

Calculate spring force, displacement, or spring constant using Hooke's Law formula F = -kΔx

Calculate Using Hooke's Law

Calculate displacement from initial and final spring lengths

N/m

Stiffness of the spring (resistance to deformation)

m

Distance spring is stretched or compressed

Hooke's Law Results

0.00
Spring Force (N)
0.00
Spring Constant (N/m)
0.000
Displacement (m)

Formula used: F = -kΔx (absolute value shown)

Note: The negative sign indicates the restoring force acts opposite to displacement

Elastic PE formula: PE = ½kx²

Example Calculation

Spring Force Problem

Given:

• Spring constant (k) = 80 N/m

• Displacement (Δx) = 0.15 m (stretched)

Find: Spring force (F)

Solution

Using Hooke's Law: F = kΔx

F = 80 N/m × 0.15 m

F = 12 N

Note: Actual force direction is opposite to displacement (restoring force)

Spring Stiffness Guide

S

Soft Springs

k < 100 N/m

Easy to stretch/compress

M

Medium Springs

100-1000 N/m

Moderate resistance

H

Stiff Springs

k > 1000 N/m

High resistance to deformation

Hooke's Law Tips

Force is proportional to displacement for elastic springs

Restoring force always acts opposite to displacement

Higher spring constant means stiffer spring

Hooke's Law applies only within elastic limit

Energy stored in spring = ½kx²

Understanding Hooke's Law

What is Hooke's Law?

Hooke's Law describes the relationship between the force applied to an elastic object (like a spring) and the resulting displacement. It states that the force is proportional to the displacement, provided the elastic limit is not exceeded.

Key Principles

  • Force is directly proportional to displacement
  • Restoring force opposes the applied force
  • Spring constant determines stiffness
  • Only valid within elastic limit

Formula Explanation

F = -kΔx

  • F: Spring force (Newtons, N)
  • k: Spring constant (N/m)
  • Δx: Displacement from equilibrium (meters, m)
  • Negative sign: Indicates restoring force direction

Remember: The larger the spring constant (k), the stiffer the spring and the more force required for the same displacement.

Elastic Potential Energy

When a spring is compressed or stretched, it stores elastic potential energy. This energy can be calculated using the formula PE = ½kx², where the energy is proportional to the square of the displacement.

Applications of Hooke's Law:

  • • Automotive suspension systems
  • • Mechanical scales and balances
  • • Elastic materials and rubber bands
  • • Shock absorbers and dampers
  • • Watch springs and clockwork
  • • Trampolines and bungee cords