Hooke’s Law Explained

Categories: Springtelligence|532 words|2.7 min read|By |Published On: June 20th, 2018|

Hooke’s Law is the proportional relationship between the force impacting a spring and the distance the spring extends or compresses.

Hooke was a founding member and curator of the Royal Society. Incredibly intelligent, he intuitively grasped amazing scientific truths without always understanding the hard science beneath.

The 1678 publication of Hooke’s Lectures of Spring shared his theory of elasticity; now known as “Hooke’s Law”.

Hooke’s Law states an elastic object must return to its original shape and size after removing the force from the load. Similarly, the law explains if a spring is overstretched it will not return to its original position upon removal of the force, as it exceeds the elastic limit. This is plastic deformation.

Hooke’s Law is expressed using the equation F = k × x (also written as F = kx).

  • F is the force in newtons (N)
  • k is the ‘spring constant’ in newtons per metre (N/m)
  • x is the extension in metres (m)

Spring Constant and Hooke’s Law

Springs have their own natural “spring constant” which defines how stiff they are. The constant of a spring (k) can vary depending on material type, spring diameters, wire thickness and total active coils.

According to Newton’s Third Law of Motion, springs apply a restoring force when pulled. This follows Hooke’s Law – the relationship between the spring force and spring constant, and the spring displacement.

The law is applicable not just to springs, but also to the majority of solid elastic objects – as long as the forces are small enough to remain within the elastic limit.

How to calculate spring constant

To calculate the spring constant, you need to measure the unloaded length of a spring, then add weights of slotted masses and calculate the changes at each interval.

The graph below demonstrates Hooke’s Law, showing an extension plotted against a force. To measure spring constant, you must use the force of the extension to allow the line to go through the origin. The gradient of a spring’s constant (k) can change depending on the stiffness of a spring. This means the graph will look different if any of the factors mentioned above change.

Hooke's Law

Equilibrium Position

A spring will have an equilibrium position of 0 when x = 0. However, F = k x e is only possible if the spring has a force pushing or pulling it from one direction, e.g. left, right, up or down.


If you’re interested in learning more information about springs, visit the Springtelligence section of our website where you’ll find interactive educational tools and resources on compression spring, tension spring and torsion spring engineering and manufacturing. Alternatively, to learn more about Robert Hooke and his work with springs, visit our other Robert Hooke blog posts:
10 Facts You Probably Didn’t Know About Robert Hooke
What Did Robert Hooke Discover