Spring Force Calculator – Hooke's Law
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Spring Force Calculator

Calculate spring force, spring constant, or displacement using Hooke's law. Enter your values, choose the appropriate units, and get an instant physics result.

Calculate Spring Force

Hooke's Law The restoring force of an ideal spring is proportional to its displacement from equilibrium.

Spring Calculation Result

Spring Force
0 N
Formula Used F = −kx
Force Magnitude 0 N
Spring Constant 0 N/m
Displacement 0 m
Elastic Potential Energy 0 J
/\/\/\/\/\/\/\/\/\
MASS
x
The negative sign in Hooke's law means that the restoring force acts in the opposite direction to displacement.

What Is a Spring Force Calculator?

A Spring Force Calculator is a physics tool used to calculate the restoring force produced when a spring is stretched or compressed. It is based on Hooke's law, which relates force, spring stiffness, and displacement.

Within its elastic range, an ideal spring produces a force proportional to the amount it is stretched or compressed. A stiffer spring has a larger spring constant and therefore requires more force for the same displacement.

This calculator can solve for spring force, spring constant, or displacement. It also calculates the elastic potential energy stored in the spring.

Spring Force Formulas

Spring Force F = −kx

Calculates the restoring force generated by the spring.

Spring Constant k = |F| / |x|

Calculates spring stiffness from force and displacement.

Displacement |x| = |F| / k

Calculates the amount of spring compression or extension.

Elastic Potential Energy U = ½kx²

Calculates the energy stored in the deformed spring.

Hooke's Law Symbols

F — Spring Force

The restoring force produced by the spring, measured in newtons.

k — Spring Constant

A measure of the spring's stiffness, normally expressed in newtons per meter.

x — Displacement

The distance the spring is stretched or compressed from its equilibrium position.

U — Elastic Energy

The elastic potential energy stored in the spring, measured in joules.

How to Use the Spring Force Calculator

1

Select a Calculation

Choose Spring Force, Spring Constant, or Displacement.

2

Enter Known Values

Enter the two known quantities required for the selected calculation.

3

Select Units

Choose the appropriate force, spring constant, and distance units.

4

Calculate

Click Calculate to instantly see the answer and related spring values.

Spring Force Calculation Example

Suppose a spring has a spring constant of 200 N/m and is stretched by 0.05 meters.

F = −kx F = −200 × 0.05 F = −10 N

The magnitude of the spring force is therefore 10 N. The negative sign indicates that the force acts opposite to the direction in which the spring was displaced.

Its elastic potential energy is:

U = ½kx² U = ½ × 200 × 0.05² U = 0.25 J

What Is the Spring Constant?

The spring constant indicates how stiff a spring is. A higher spring constant means more force is required to produce the same displacement.

For example, a 500 N/m spring is stiffer than a 100 N/m spring. The standard SI unit of spring constant is newtons per meter.

Hooke's law is most accurate while a spring remains inside its elastic range. Once a real spring is deformed beyond this range, its force-displacement relationship may no longer be linear.

Frequently Asked Questions

The spring force equation is F = −kx, where k is the spring constant and x is displacement from equilibrium.

The negative sign shows that the restoring force acts in the opposite direction to the spring's displacement.

The standard SI unit of spring constant is newtons per meter, written as N/m.

The magnitude of spring displacement can be calculated using x = F/k when force magnitude and spring constant are known.

Elastic potential energy is calculated using U = ½kx².

Hooke's law is an ideal linear model and is most accurate while a spring remains within its elastic operating range.