The linear strain is the ratio of change in length to the original length.
The length is shortened in the direction of the forces when the forces are compressive. This is called the linear strain or Compressive Strain . If the change in length is ‘ l ‘ in a wire or bar of original length L,
the formula for Linear strain or longitudinal strain is given as,

Linear Strain or Compressive Strain = Change in length / Original Length

Linear Strain or Compressive Strain =  Δ l / L

The change in length can be an increase or decrease.
As the linear strain is ratio of lengths,it has no unit and dimension.

When an external deforming force applied on the body it produces change in shape of body which is known as shearing stress.

The formula for shearing stress is given as,

Shearing Stress = tangential applied Force / Area

Shearing Stress = F/A

In the above figure Shearing Force F1 is applied to one face of Square which causes deformity in square known as Shearing Stress

When an external deforming force is applied on the body it produces change in volume of body which is known as volume or bulk stress.

The formula for bulk or volume stress is given as,

Bulk Stress or Volume Stress = Change in magnitude of Force / Area

We know that Force can also be expressed as Force = Pressure x Area

Bulk Stress or Volume Stress = Change in Pressure / Area

Bulk Stress or Volume Stress = Change in Pressure (Δ P)

Bulk Stress or Volume Stress = Δ P

When an external deforming force applied on the body produces change in length of body then it is longitudinal or tensile stress.
The formula for longitudinal or tensile stress is given as,

Tensile Stress = Force / Area

Longitudinal Stress is often seen in cylinder, pipe , wire etc. So we can also write it as,

Longitudinal Stress = Force/ Area

Longitudinal Stress = F / π r ²

we know that force can also be defined as Force = mass x acceleration due to gravity

Longitudinal Stress = m g/ π r ²

where m = unit length of mass, g= acceleration due to gravity and r= radius.

Internal restoring force per unit area of the body on which it acts is stress. Deformation happens (change in shape or in size or both) when an external force is acting on an elastic body. There is equal and opposite force developed inside the body to bring the body back to its original shape. This force is known as the restoring force.

The formula for stress is given as,

Stress = Applied Force / Area

Stress = F /A

The unit for stress is newton metre^-2 with symbol N m^-2 or ‘pascal’ with symbol  ‘Pa’.