 Spring displacement (Δx)
ft
Spring force constant (k)
N/m
Force (F)
N

# Hooke's Law Calculator

By Bogna Haponiuk

We created the Hooke's law calculator (spring force calculator) to help you determine the force in any spring that is stretched or compressed. You can also use it as a spring constant calculator if you already know the force. Read on to get a better understanding of the relationship between these values and to learn the spring force equation.

## Hooke's law and spring constant

Hooke's law deals with springs and their main property - the elasticity. Each spring can be deformed (stretched or compressed) to some extent. When the force that causes the deformation disappears, the spring comes back to its initial shape, provided the elastic limit was not exceeded.

Hooke's law states that for an elastic spring, the force and displacement are proportional to each other. It means that as the spring force increases, the displacement increases, too. If you graphed this relationship, you would discover that the graph is a straight line. Its inclination depends on the constant of proportionality, called the spring constant. It always has a positive value.

## Spring force equation

Knowing Hooke's law, we can write it down it the form of a formula:

`F = -kΔx`

where:

• F is the spring force (in N);
• k is the spring constant (in N/m); and
• Δx is the displacement (positive for elongation and negative for compression, in m).

Where did the minus come from? Imagine that you pull a string to your right, making it stretch. A force arises in the spring, but where does it want the spring to go? To the right? If it were so, the spring would elongate to infinity. The force resists the displacement and has a direction opposite to it, hence the minus sign.

You can find the elastic potential energy of the spring, too.

## How to use the Hooke's law calculator

1. Choose a value of spring constant - for example, `80 N/m`.
2. Determine the displacement of the spring - let's say, `0.15 m`.
3. Substitute them into the formula: `F = -kΔx = -80 * 0.15 = 12 N`.
4. Check the units! `N/m * m = N`.
5. You can also use the Hooke's law calculator in advanced mode, inserting the initial and final length of the spring instead of the displacement.
6. You can now calculate the acceleration that the spring has when coming back to its original shape.

You can use Hooke's law calculator to find the spring constant, too. Try this simple exercise - if the force is equal to 60 N, and the length of the spring decreased from 15 to 10 cm, what is the spring constant?

Bogna Haponiuk