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`W = 1/2* "k" * "x" ^2`

Enter a value for all fields

The **Work to Stretch or Compress a Spring** calculator compute the work based on the spring constant (k) and the displacement (x).

**INSTRUCTIONS:** Choose units and enter the following:

- (
**k**) - Spring constant characterizing a spring's stiffness or elasticity in units of newtons per meter (N/m) - (
**x**) - Distance the spring is either stretched or compressed

**Work on a Spring (W):** The calculator returns the work in newton meters (N*m)

The formula for the Work to Stretch or Compress a Spring is:

W = 1/2 k ⋅ x^{2}

Hooke's Law defines the force used to displace a spring as: F = -k*x. The minus sign conveys that this is a restorative force acting in opposition to the spring being stretched or compressed.

And then we know that **energy** is defined to be the ability to do **work**, so there is a direct relationship between **energy** and **work**.

We know that **work** is **force** over a **distance** and in this case the **force** required to extend (or compress) the spring increases linearly with distance according to our spring-force equation F = -k*x (Hooke's Law ). In other words, the more you stretch a spring the harder it gets to stretch it a little farther.

We also know that the **work** done to compress (or stretch) the spring is equal to the potential energy the spring possesses once the spring is fully extended (compressed) by some distance, **x**. If we look at the force versus distance graph, we can intuit from out basic knowledge of calculus that the area under the graph of force versus distance is the total work performed. And we can find that area under the graph by integrating the force over the distance **x**.

So, `W = U = int F*dx = int(k*x*dx) = (1/2) * k*x^2` and this is the **total work** to compress the spring by a distance, **x**, and thus is also equivalent to the **potential energy** stored in the compressed (or stretched) spring.

The standard SI units for potential energy are newton-meters which are equivalent to Joules.

Khan Academy's Potential energy stored in a spring

Khan Academy's Spring potential energy example shows a nice example of applying the potential energy equation for a spring