# Spring Constant Formula

According to Hooke’s law, the force required to compress or extend a spring is directly proportional to the distance it is stretched. It can be represented in an equation as F = kx, where F is the force applied, k is the spring constant and x is the extension of the object usually in meters.

In other words, spring constant is the force applied if the displacement in the spring is unity.

If a force F is considered that stretches the spring so that it displaces the equilibrium position by x.

The Spring Constant Formula is given as,

$K\,&space;=\,&space;-\frac{F}{X}$

Where,

F = Force applied,

x = displacement by the spring

It is expressed in Newton per meter (N/m).

### Solved Examples

Example 1

A spring with load 5 Kg is stretched by 40 cm. Determine its spring constant.

Solution:

Given:

Mass m = 5 Kg,

Displacement x = 40 cm,

We know that,

Force F = m a

= 5 × 0.4

= 2 N

The spring constant is given as

k = – F / x

= – 2 / 0.4

= – 5 N/m

Example 2

A boy weighing 20 pounds stretches a spring by 50 cm. Determine the spring constant of the spring.

Solution:

Given:

Mass m = 20 lbs = 20 / 2.2 = 9.09 Kg.

Displacement x = 50 cm

The force F = ma = 9.09 × 9.8 = 89.082 N

The spring constant formula is given by

k = – F / x

= – 89.082 / 0.5

= – 178.164 N/m.