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
negative sign indicates it is acting towards the center
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
$x=\sqrt {\frac {2U}{k}}$
