Hooke's Law Calculator

Hooke's Law Formula: F = -k × x

F = Force applied to spring (N) | k = Spring constant (N/m) | x = Displacement from equilibrium (m)

Spring Constant (k)

N/m

Stiffness of the spring

Displacement (x)

Distance stretched or compressed

Force (F)

Applied force on the spring

Unit System

SI Units (N, m, N/m)

Imperial (lb, in, lb/in)

Custom Units

Calculated Result

0.00 N

Enter any two values to calculate the third.

Spring Constant (k): 0.00 N/m

Displacement (x): 0.00 m

Force (F): 0.00 N

Spring Visualization

Equilibrium: 0.00 m

Displacement: 0.00 m

Calculation History

Spring Force Just now

k=50.00 N/m, x=0.10 m → F=5.00 N

Spring Properties

Spring Type

Material

Spring Length

Wire Diameter

Coils Count

coils

About Hooke's Law

Hooke's Law states that the force needed to extend or compress a spring by some distance is proportional to that distance. The law is named after 17th-century British physicist Robert Hooke.

Key Points:

The spring force is a restoring force
It acts in the opposite direction to displacement
Valid within the elastic limit of the material
Linear relationship between force and displacement

Applications:

Spring scales and balances
Vehicle suspension systems
Mechanical watches
Shock absorbers
Mattresses and upholstery

Elastic Limit

Hooke's Law only applies within the material's elastic limit. Beyond this point, the spring will deform permanently.

Negative Sign

The negative sign in F = -kx indicates the restoring force is opposite to the displacement direction.

How to Use the Hooke's Law Calculator: A Complete Guide

This comprehensive Hooke's Law calculator helps students, engineers, and physics enthusiasts quickly calculate spring parameters in real-time. Here's how to get the most out of this tool:

Step-by-Step Guide:

Enter Known Values: Input any two of the three parameters (Spring Constant, Displacement, or Force). The calculator will automatically compute the missing value in real-time.
Select Unit System: Choose between SI units (Newtons, meters) or Imperial units (pounds, inches) based on your requirements.
Review Results: The calculated value appears instantly with a visual spring representation showing the displacement.
Save Calculations: Click "Save Calculation" to store results in the history panel for future reference.
Adjust Spring Properties: Use the Spring Properties section to estimate spring constant based on material and physical dimensions.

Practical Example:

Suppose you have a spring with a constant of 200 N/m and you stretch it by 0.05 meters. Enter these values in the calculator, and it will instantly compute the force as 10 Newtons. The visualization will show the spring stretched accordingly.

Advanced Features:

Real-time Visualization: Watch the spring visualization update as you change input values.
Calculation History: All your calculations are saved automatically for comparison and reference.
Spring Constant Estimation: Estimate the spring constant based on material properties and physical dimensions.
Export Functionality: Download your calculation history as a CSV file for analysis in spreadsheet software.
Unit Conversion: Switch between different unit systems with a single click.
Share Results: Easily share your calculations with colleagues or classmates.

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Did You Know?

Robert Hooke first stated his law in 1660 as a Latin anagram "ceiiinosssttuv". He later published the solution in 1678 as "Ut tensio, sic vis" meaning "As the extension, so the force".