Hooke's Law Calculator

General Physics

Calculate force, spring constant, or displacement based on Hooke's Law.

N
N/m
m
Examples

Explore some real-world scenarios for using the Hooke's Law calculator.

Calculate Force

force

A spring with a constant of 200 N/m is stretched by 0.25 m. Find the force exerted by the spring.

k: 200 N/m

x: 0.25 m

Calculate Spring Constant

springConstant

A force of 150 N stretches a spring by 0.5 m. What is the spring constant?

F: 150 N

x: 0.5 m

Calculate Displacement

displacement

A spring with a stiffness of 500 N/m has a force of 100 N applied to it. How far will it stretch?

F: 100 N

k: 500 N/m

Car Suspension

force

A car's suspension spring has a constant of 25000 N/m. If it compresses by 0.1 m when a person gets in, what force is exerted?

k: 25000 N/m

x: 0.1 m

Other Titles
Understanding Hooke's Law: A Comprehensive Guide
An in-depth look at the principles of elasticity, spring force, and potential energy.

What is Hooke's Law?

  • The Core Formula: F = -kx
  • Understanding the Components
  • The Concept of Elasticity and the Elastic Limit
Hooke's Law is a fundamental principle in physics and engineering that describes the relationship between the force applied to a spring and the resulting displacement. It states that the force (F) required to stretch or compress a spring by some distance (x) from its equilibrium position is directly proportional to that distance. The law is named after the 17th-century British physicist Robert Hooke.
The Core Formula: F = -kx
The mathematical representation of Hooke's Law is F = -kx. Here, 'F' is the restoring force exerted by the spring, 'k' is the spring constant, and 'x' is the displacement. The negative sign indicates that the restoring force is always in the opposite direction of the displacement. For example, if you pull a spring to the right, it will exert a force to the left to return to its original shape. Our calculator typically ignores the negative sign to focus on the magnitude of the force.
The Elastic Limit
It's crucial to understand that Hooke's Law is only valid within the 'elastic limit' of the material. If a spring is stretched beyond this point, it becomes permanently deformed and will not return to its original shape. All calculations assume you are operating within this limit.

Simple Example

  • If a spring with a constant k = 100 N/m is stretched by x = 0.2 m, the force it exerts is F = 100 * 0.2 = 20 N.

Step-by-Step Guide to Using the Hooke's Law Calculator

  • Selecting the Calculation Type
  • Entering Input Values
  • Interpreting the Results
Our calculator simplifies Hooke's Law problems by allowing you to solve for any of the main variables.
1. Select the Calculation Type
Start by using the dropdown menu to choose what you want to calculate: Force (F), Spring Constant (k), or Displacement (x).
2. Enter the Known Values
Fill in the two fields for the variables you know. For instance, if you're calculating Force, you'll need to input the Spring Constant and Displacement. Ensure your inputs are positive numbers.
3. Interpret the Results
After clicking 'Calculate', the tool will display the result for your chosen variable. It will also show the Elastic Potential Energy stored in the spring, which is calculated using the formula U = 1/2 * kx².

Real-World Applications of Hooke's Law

  • Mechanical Engineering
  • Physics Education
  • Material Science
Hooke's Law is not just a textbook formula; it's applied in countless real-world devices and systems.
Automotive Suspension
The springs in a car's suspension system are designed using Hooke's Law. They absorb shock from bumps in the road, and their spring constant is carefully chosen to provide a smooth ride without excessive bouncing.
Everyday Objects
From the retractable mechanism in a ballpoint pen to the springs in a mattress or a trampoline, Hooke's Law governs how these objects function. It is also fundamental to the design of mechanical scales and force-measuring devices.

Common Misconceptions and Correct Methods

  • The Negative Sign
  • Units of Measurement
  • Linearity Assumption
The Directional Negative Sign
A common point of confusion is the negative sign in F = -kx. This sign simply indicates that the restoring force opposes the displacement. When calculating the magnitude of the force, the sign is often dropped. The calculator focuses on magnitude, so you don't need to input negative values.
Consistency in Units
For the formula to work correctly, units must be consistent. The standard SI units are Newtons (N) for force, meters (m) for displacement, and Newtons per meter (N/m) for the spring constant. Using inconsistent units (e.g., centimeters for displacement with a spring constant in N/m) will lead to incorrect results if not converted properly.

Mathematical Derivation and Examples

  • Deriving Potential Energy
  • Worked Example: Finding k
  • Worked Example: Finding U
Deriving Elastic Potential Energy (U)
The work done to stretch a spring is stored as elastic potential energy. This can be derived by integrating the force function F(x) = kx with respect to x. The work (W) is ∫(kx) dx, which evaluates to 1/2 kx². Therefore, the stored potential energy U = 1/2 kx².
Worked Example: Finding k
Suppose a 5 kg mass is hung from a spring, causing it to stretch by 10 cm. First, find the force (weight): F = mg = 5 kg * 9.8 m/s² = 49 N. The displacement is x = 10 cm = 0.1 m. Now, find the spring constant: k = F / x = 49 N / 0.1 m = 490 N/m.