$F= -kx$

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

$k= \frac {2U}{x^2}$

- 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.

$ F = Kx$

A spring equilibrium position is stretched by .2 m and force exerted by spring is 10 N. Find the spring constant

Given x=.2 m, F= 10 N, k=? Spring constant formula is given by

$k = \frac {F}{x}$

$k = \frac {10}{.2}= 50 \ N/m$

A spring was stretched by .1 m and spring constant is 100 N/m. Find the Force exerted.

Given x=.1 m, F= ?, k=100 N/m As per Hooke's law

$F= -kx$

$F = 100 \times .1= 10 \ N$

- 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

$x=\frac {F}{k}$

- 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.

$U = \frac {1}{2}Kx^2$

The potential energy in stretched spring is 81J and displacement is .8 m. Calculate spring constant

Given, U=81 J, x=.8 m, k=?

Spring constant will be given as

$k= \frac {2U}{x^2}= \frac {2 \times 81}{.64} =253.1 \ N/m$

Calculate the displacement if potential energy is 72 J and Spring constant is 100 N/m?

Given, U=72 J, x=?, k=100 N/m

Displacement would be given as

$x=\sqrt {\frac {2U}{k}}= \sqrt { \frac {2 \times 72}{10}}= .379 \ m$

- 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

$x=\sqrt {\frac {2U}{k}}$

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