Poisson’s Ratio:

When an object is elongated longitudinally in the direction of the tensile force, then there will be a lateral contraction. this means that the contraction is in a direction perpendicular to the direction of tensile force. The ratio of lateral strain to longitudinal strain within the elastic limit is called Poisson’s Ratio \( (\sigma) \).

Let us consider a wire of length \( L \) and diameter \( D \), undergoes an eleongation \( l \) along the direction of applied tensile force \( F \), and also undergoes a contraction of amount \( d \) along the direction perpendiculer to the direction of tensile force \( F \). Then Poisson’s Ratio wil be

\sigma=\frac{Lateral\ Strain}{Longitudinal\ Strain} 
\\=\frac{d/D}{l/L}
\\=\frac{d\cdot{L}}{l\cdot{D}}

Is Poisson’s Ratio an Elastic Modulus?

Poisson’s ratio is not an elastic modulus as it is the ratio of two types of strains, not the ratio of stress to strain. It is a dimensionless pure number.