Hooke's Law Calculator

What is Hooke's Law?

If you pull on a rubber band, it stretches. If you pull harder, it stretches more. This simple intuition is the basis of Hooke's Law.

Discovered by British physicist Robert Hooke in 1660 (initially published as an anagram to claim the discovery before revealing the math), the law states that the force needed to extend or compress a spring is directly proportional to the distance it moves.

The negative sign indicates that the spring force is a "Restoring Force"—it always pulls in the opposite direction of the displacement to try and get back to its resting shape.

The Variables Explained

• F (Force): The effort applied to stretch/compress the spring. Measured in Newtons (N).
• x (Displacement): The distance the spring moves from its equilibrium (resting) position. Not the total length of the spring, just the change in length. Measured in Meters (m).
• k (Spring Constant): This is the "Stiffness" of the spring. A high k means the spring is stiff (like a car suspension). A low k means it is loose (like a Slinky). Measured in N/m.

Elastic Potential Energy (Storing Power)

When you compress a spring, you aren't just moving metal; you are storing energy. This is how wind-up toys, mechanical watches, and even dart guns work.

The energy stored in the spring is not linear (like force); it is exponential. If you stretch a spring twice as far, you store four times as much energy.

Formula: PE = ½ kx²

Our calculator automatically computes this "Potential Energy" (PE) for you in Joules every time you run a calculation.

When Does Hooke's Law Fail?

Hooke's Law describes the "Elastic Region" of a material. This is the zone where, if you let go, the material snaps back to its original shape.

However, if you pull a spring too hard, you will permanently warp it. This is called the Limit of Proportionality or the "Plastic Region." Once you cross this threshold, Hooke's Law no longer applies, and the spring is broken.

How to Find the Spring Constant (k)

If you have a mystery spring and want to know its stiffness (k), you can perform a simple experiment at home:

1. Hang the spring vertically and measure its length.
2. Hang a known mass (e.g., 1kg) from the bottom.
3. Measure the new length.
4. Calculate x (New Length - Old Length).
5. Calculate Force (F) using F = Mass × Gravity (9.8).
6. Solve for k: k = F ÷ x.

Common Spring Constants