Spring Constant Calculator

How to Calculate Spring Force, Constant, and Displacement

Understanding the relationship between spring force, spring constant, and displacement is fundamental in physics and engineering. This calculator helps you determine any one of these variables when you know the other two.

What is the Formula?

The basic formula relating spring force, spring constant, and displacement is Hooke's Law:

\[ F = -kx \]

Where:

• F is the spring force (in Newtons, N)
• k is the spring constant (in Newtons per meter, N/m)
• x is the displacement from the equilibrium position (in meters, m)

From this, we can derive two other formulas:

\[ k = \frac{F}{x} \]

\[ x = \frac{F}{k} \]

What are the calculation steps?

1. Identify which two variables you know and which one you need to calculate.
2. Ensure all units are consistent (convert if necessary).
3. Apply the appropriate formula based on what you're calculating.
4. Perform the calculation to get your result.

Example Calculation

Let's calculate the spring force:

Given:

• Spring constant (k) = 100 N/m
• Displacement (x) = 0.05 m

Step 1: Identify the formula

We need to calculate force, so we'll use: F = kx

Step 2: Plug in the values

F = 100 N/m * 0.05 m

Step 3: Perform the calculation

F = 5 N

Therefore, the spring force is 5 Newtons.

Diagram of Spring Force, Constant, and Displacement Relationship

The following diagram illustrates the relationship between spring force, spring constant, and displacement:

This diagram shows how spring force (F) is related to the spring constant (k) and displacement (x). The top line represents the spring at rest, while the bottom line shows the spring when it's stretched or compressed. The formula F = k * x encapsulates this relationship, where the force is proportional to the displacement, with the spring constant as the proportionality factor.