Hooke's Law Calculator

Category: Physics

- April 04, 2025

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Calculate force, spring constant, or displacement using Hooke's Law, which states that the force exerted by a spring is proportional to its displacement from equilibrium.

What do you want to calculate?

Force (F)

Spring Constant (k)

Displacement (x)

Enter Spring Constant

Spring Constant (k):

Enter Displacement

Displacement (x):

Advanced Options

Decimal Places:

Show Calculation Steps

Show Visualization

Calculate Elastic Potential Energy

About Hooke's Law

Hooke's Law describes the relationship between the force exerted by a spring and the displacement of the spring from its equilibrium position. The law states that the force is proportional to the displacement, with the spring constant (k) as the proportionality factor.

The Formula

The mathematical representation of Hooke's Law is:

F = -k × x

Where:

F is the restoring force exerted by the spring (in Newtons, N)
k is the spring constant, a measure of the spring's stiffness (in Newtons per meter, N/m)
x is the displacement of the spring from its equilibrium position (in meters, m)
The negative sign indicates that the force is in the opposite direction to the displacement

Note: In this calculator, we use the magnitude of the force, so we omit the negative sign.

Elastic Potential Energy

A spring that obeys Hooke's Law stores elastic potential energy when it is stretched or compressed:

U = ½ × k × x²

Where U is the elastic potential energy (in Joules, J).

Limitations

Hooke's Law is only valid within the elastic limit of the material. Beyond this limit, the spring will deform permanently and no longer return to its original shape when the force is removed.

Applications

Engineering: Spring design in mechanical systems, seismic isolators
Physics: Studying oscillatory motion, harmonic oscillators
Materials Science: Analyzing material properties and elasticity
Automotive: Suspension systems, shock absorbers
Everyday items: Mattresses, trampolines, pogo sticks

What Is the Hooke's Law Calculator?

The Hooke's Law Calculator helps you figure out the relationship between force, spring constant, and displacement in a spring system. It uses Hooke's Law to make quick and accurate calculations without the need for manual effort.

This tool is perfect for students, engineers, educators, or anyone dealing with mechanical systems that involve springs.

Hooke’s Law:
F = k × x

Elastic Potential Energy:
U = ½ × k × x²

What Does It Calculate?

You can use the calculator to find out any one of the following, based on the other two:

Force (F): The restoring force exerted by the spring
Spring Constant (k): A measure of how stiff the spring is
Displacement (x): How much the spring is stretched or compressed

Additionally, it can calculate the elastic potential energy stored in the spring.

How to Use the Calculator

Select what you want to calculate: Force, Spring Constant, or Displacement.
Enter the known values in the input fields. Use the unit selectors to switch between different measurement units.
Choose how many decimal places you want in the results.
Optional: Tick the boxes to show calculation steps, visualisations, or energy output.
Click Calculate to see results instantly.
Click Reset to clear the fields and start afresh.

Key Features

Supports multiple units for force, displacement, and spring constant
Displays formulas and step-by-step breakdowns for learning
Includes a visual diagram of the spring system
Calculates elastic potential energy if needed
User-friendly and responsive design

Why Use This Tool?

Manual calculations can take time and may lead to errors, especially when converting units or dealing with energy equations. This calculator removes the guesswork and speeds up the process by providing you with:

Accurate results in seconds
Visual feedback to reinforce understanding
Insight into how variables relate to one another

Whether you're finishing a homework assignment, designing a mechanical component, or just curious, this tool gives you the clarity you need.

Frequently Asked Questions (FAQ)

What is Hooke's Law?

Hooke’s Law describes how springs behave. It states that the force exerted by a spring is directly proportional to its displacement from the rest position, within the elastic limit.

What units can I use?

You can input and display values in various units, including:

Force: N, lbf, kgf, dyn
Spring Constant: N/m, N/cm, lbf/in, lbf/ft
Displacement: m, cm, mm, in, ft

What does the "elastic potential energy" option do?

When enabled, the calculator will also compute the energy stored in the spring due to deformation, using the formula:

U = ½ × k × x²

Can I see how the values are calculated?

Yes. Just tick the box labelled “Show Calculation Steps” and you'll see a clear breakdown of how the result was reached.

Is this calculator suitable for real-world applications?

Yes, as long as the spring system stays within its elastic limit. Beyond that point, the spring may deform permanently and the law no longer applies.

Conclusion

The Hooke’s Law Calculator is a practical and straightforward way to explore how springs behave under force. Whether you need to solve a physics problem, model a system, or just want to understand spring mechanics better, this tool provides results quickly and clearly.