# Spring Constant calculator

## what is spring constant

As per Hooke's law, The restoring force applied by the spring is proportional to change in length and restoring force is directed towards the equilibrium position. The proportionality constant is called the spring constand and it is basically a measure of the stiffness of the spring. So as Hooke's law
$F= -kx$
Where
F -> Restoring force
K-> Spring constant
x -> change in length
Rearranging this for Spring constant, Spring constant formula is given by
$k = \frac {F}{x}$
Unit of Spring Constant is Newton/meter
It is also possible to calculate Spring constants using Elastic Energy equation. It is given as
$U= \frac {1}{2} kx^2$
where
U -> Potential energy or elastic energy
k-> Spring constant
x -> change in length
Spring constant will be given as
$k= \frac {2U}{x^2}$

## Spring Constant Calculator using Hooke's law

Note
• Enter the values of the two known variables in the text boxes
• Leave the text box empty for the variable you want to solve for
• Click on the calculate button.
The formula used for solving the question is Hooke's Law
$F = Kx$

### Spring Constant Calculator

Example of Few questions where you can use this formula
Question 1
A spring equilibrium position is stretched by .2 m and force exerted by spring is 10 N. Find the spring constant
Solution
Given x=.2 m, F= 10 N, k=? Spring constant formula is given by
$k = \frac {F}{x}$
$k = \frac {10}{.2}= 50 \ N/m$

Question 2
A spring was stretched by .1 m and spring constant is 100 N/m. Find the Force exerted.
Solution
Given x=.1 m, F= ?, k=100 N/m As per Hooke's law
$F= -kx$
$F = 100 \times .1= 10 \ N$

## How this Spring constant calculator works

• if displacement and Force is given,spring constant is calculated as
$k= \frac {F}{x}$
• if displacement and spring constant is given,force is calculated as
$F=Kx$
• if force and spring constant is given,displacement is calculated as
$x=\frac {F}{k}$

## Spring Constant Calculator using Potential energy/Elastic Energy equation

Note
• Enter the values of the two known variables in the text boxes
• Leave the text box empty for the variable you want to solve for
• Click on the calculate button.
The formula used for solving the question is
$U = \frac {1}{2}Kx^2$

### Spring Constant Calculator

Example of Few questions where you can use this formula
Question 1
The potential energy in stretched spring is 81J and displacement is .8 m. Calculate spring constant
Solution
Given, U=81 J, x=.8 m, k=?
Spring constant will be given as
$k= \frac {2U}{x^2}= \frac {2 \times 81}{.64} =253.1 \ N/m$

Question 2
Calculate the displacement if potential energy is 72 J and Spring constant is 100 N/m?
Solution
Given, U=72 J, x=?, k=100 N/m
Displacement would be given as
$x=\sqrt {\frac {2U}{k}}= \sqrt { \frac {2 \times 72}{10}}= .379 \ m$

## How this Spring constant using potential energy formula calculator works

• if displacement and Potential energy is given,spring constant is calculated as
$k= \frac {2U}{x^2}$
• if displacement and spring constant is given,Potential energy is calculated as
$U=\frac {1}{2} Kx^2$
• if Potential energy and spring constant is given,displacement is calculated as
$x=\sqrt {\frac {2U}{k}}$