Hooke’s Law Explained

Hooke’s Law Explained

By | 2018-06-21T09:25:30+00:00 June 20th, 2018|

Robert Hooke was a British physicist who stated that there is a proportional relationship between the force required to extend or compress a spring, and the distance that the spring is extended or compressed.

Hooke was a founding member and curator of experiments at the Royal Society – a society traditionally at the cutting edge of scientific discovery in Britain. He also had a knack of intuitively grasping amazing scientific truths without always understanding the hard science beneath.

The 1678 publication of Hooke’s Lectures of Spring shared his theory of elasticity; in what came to be known as “Hooke’s Law”.

This law is expressed in the below equation and states that for an object to be elastic, it must be able to return to its original shape and size, after the force has been removed from the load. Similarly, the law explains if a spring is overstretched it will not return to its original position once the force is removed as the elastic limit would have been exceed. This is known as plastic deformation.

F = k × e

  • F is the force in newtons, N
  • k is the ‘spring constant’ in newtons per metre, N/m
  • e is the extension in metres, m

A Spring’s Constant

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.

By Newton’s Third Law of Motion, as a spring is pulled, it pulls back with a restoring force. This force follows Hooke’s Law, which relates the force of the spring to the spring constant, and the displacement of the spring from its original position.

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

How can a spring’s constant be measured?

To discover a spring’s constant, an experiment will need to be carried out to identify the measurement. One way this can be discovered is by, firstly, measuring the unloaded length of a spring, then adding weights of slotted masses to the spring and calculating the measurement changes at each interval.

This graph demonstrates Hooke’s Law, showing an extension that has been plotted against a force. If a measurement of a spring is to take place, the force of the extension must be used 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, so the graph will look different if any of the factors mention above are changed.

Hooke's Law

Equilibrium Position

A spring will have an equilibrium position of 0 when x = 0. However, the formula F = k x e will only be possible if the linear spring has got a force pushing or pulling it from one direction, for instance left or right or up and 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 spring engineering and manufacturing.

Contact Info

John Binns & Son (Springs) Ltd. Airedale Business Centre, Ghyll Way, North Yorkshire, Skipton BD23 2DD, For Sat Nav please use BD23 2TZ

Phone: 01756 797979