Modulus of elasticity (
) and the modulus of rigidity (
) are related by the following equation:
Here, 
represents a number called Poisson’s ratio given to the particular material. When the material is being stretched in one direction, it gets shortened in a perpendicular direction. In the direction that the material becomes elongated, the axial strain (
) is defined as the fractional increase in the length. In the direction that the material shortens, the transverse strain (
) gives the fractional reduction in length. The diagram below illustrates these changes in shape:
Defining Poisson’s ratio
In this diagram, the axial strain is:
The transverse strain is:
Note that since the object shortens in the direction perpendicular to the force, 
. Poisson’s ratio () is defined as:
The minus sign has been introduced to ensure that takes a positive value.
