**Physics Calculators** ▶ Spring Constant Calculator

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**Table of Content**

An online spring constant calculator helps you to determine the spring constant, displacement covered by the spring and the restoring force acted upon it. The concept of the spring contraction and relaxation originates from the hooke’s law. Let’s teach you about this in detail.

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**“A particular quantity representing the stiffness of a spring is known as the spring constant”**

Let us define the basic hooke’s law that gives us the definition of the spring constant.

This law states that:

**“The restoring force by the spring is directly proportional to the change in the position and is directed towards the mean position”**

Hooke’s law equation provides the given expression for the respective formula:

$$ \text{Force} = \text{Spring Constant} * \text{Displacement} $$

$$ F = -k\delta{x} $$

$$ k = -\frac{F}{\deltax} $$

Also, we have:

$$ \deltax = -\frac{F}{k} $$

Where:

**F**= Restoring Force of the Spring- \(\deltax\) = Displacement change
- Minus sign represents that the direction of the spring is back towards the mean position

The given formula consists of few parameters that are hard to remember, thus we provides best spring constant calculator to solve particular calculations.

So what we are going to do is to solve a couple of examples to make you people ready to resolve problems related to the spring constant. Let’s go!

**Example # 01:**

A force of **21N** is applied on a spring to displace it from the mean position upto **3m**. How to calculate spring constant?

**Solution:**

We know that the spring constant equation is given as follows:

$$ k = -\frac{F}{\deltax} $$

Now here, finding the spring constant by putting all the values:

$$ k = -\frac{21}{3} $$

$$ k = 7N $$

**Example # 02:**

How to find the spring constant when a spring is stretched to a certain length of 4.23m by applying a force of 55N and then set free to go back?

**Solution:**

Using spring compression formula:

$$ k = -\frac{F}{\deltax} $$

$$ k = -\frac{55}{4.23} $$

$$ k = 13.002N $$

**Example # 03:**

Determine the restoring force of a spring when it is displaced to a length of 5m and exhibits a spring constant of 41N.

**Solution:**

We know that hooke’s law equation is as below:

$$ F = -k\delta{x} $$

$$ F = 5 * 41 $$

$$ F = 205Nm $$

Apart from the spring constant, you can also determine the restoring force by making use of hooke’s law calculator.

This free spring force calculator allows you to examine the parameters defined by the hooke’s law equation swiftly. Read on for a more comprehensive understanding of its proper use.

**Input:**

- Make a selection about the term you want to determine
- After you do so, write down the parameter values against the term selected
- Tap the calculate button

**Output:**

Depending upon the selection you made, the free hookes law calculator calculates either:

- Restoring force in the spring
- Displacement covered by the spring
- Spring constant of the spring

Following are the factors that actually affect the spring constant.

- Wire diameter
- Coil diameter
- Length of the spring

The tension in the spring wire is directly proportional to its restoring force. More the tension, the more the spring constant will be and vice versa. Keep in mind that the elongation remains unchanged.

Yes, as you increase the force to stretch a spring, the value of the spring constant also increases. Hooke’s laws helps you to determine this particular deviation in a span of seconds.

In case there are two springs that are parallel to each other, then you can easily determine the spring constraint by adding the individual spring constants of both the springs.

When the spring constant is increased, it increases the force of restoration that quickly moves the object to the mean position in less time. From this, we get to know that spring constant has an inverse relation with the time period.

A large spring constant represents that the stiffness of the spring is high. Whereas, a smaller spring constant shows that the stiffness is also lower.

Spring 3 is considered the most stiffest among all springs and hence has the largest spring constant determined so far.

Yes, the spring constant is considered as the slope of a line as it defines the relation among force and displacement on the graph.

Spring constant is a very important factor to determine the stiffness of a spring attached to any object. So if you are examining spring movements, never neglect to make the use of a spring constant calculator to acquire certainty in results.

From the source of Wikipedia: Simple harmonic motion, Dynamics, Energy, Scotch yoke

From the source of Lumen Learning: Hooke’s Law, Elastic Potential Energy