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
- Write the formula: F = kx.
- Substitute the values: F = 200 × 0.3.
- 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
Continue analyzing springs
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
Hooke's law FAQ
What formula does the Hooke’s law calculator use?
It uses F = kx, where force equals the spring constant multiplied by extension.
What is the SI unit of spring constant?
The SI unit of spring constant is newtons per meter, written as N/m.
What is extension in Hooke’s law?
Extension is the change in length from the spring’s equilibrium position.
When does Hooke’s law stop applying?
Hooke’s law applies only while the spring remains within its elastic region and its spring constant stays effectively constant.