Hooke's Law Calculator

Category: Physics
- March 22, 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?

Enter Spring Constant

Enter Displacement

Advanced Options

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 determine the relationship between force, spring constant, and displacement in a spring system. It uses Hooke's Law to make quick and accurate calculations without manual effort.

This tool is ideal for students, engineers, educators, or anyone working with mechanical systems involving springs.

Hooke’s Law:
F = k × x
Elastic Potential Energy:
U = ½ × k × x²

What Does It Calculate?

You can use the calculator to solve for 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 the stiffness of the spring
  • 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

  1. Select what you want to calculate: Force, Spring Constant, or Displacement.
  2. Enter the known values in the input fields. Use the unit selectors to switch between different measurement units.
  3. Choose how many decimal places you want in the results.
  4. Optional: Check the boxes to show calculation steps, visualizations, or energy output.
  5. Click Calculate to view results instantly.
  6. Click Reset to clear the fields and start over.

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 desired
  • User-friendly and responsive design

Why Use This Tool?

Manual calculations can take time and may lead to mistakes, especially when converting units or working with energy equations. This calculator eliminates guesswork and speeds up the process by giving you:

  • Accurate results in seconds
  • Visual feedback to reinforce understanding
  • Insight into how variables relate to each other

Whether you're completing a homework assignment, designing a mechanical component, or simply curious, this tool provides the clarity you need.

Frequently Asked Questions (FAQ)

What is Hooke's Law?

Hooke’s Law describes the behavior of springs. 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 check the box labeled “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 simple way to explore how springs behave under force. Whether you need to solve a physics problem, model a system, or just understand spring mechanics better, this tool delivers results quickly and clearly.