Poisson’s Ratio is defined as the ratio of lateral contraction to linear elongation . It can also be defined as the ratio of unit transverse (Lateral) strain to unit longitudinal strain.
Mathematically,
Poisson’s ratio (σ) = Lateral Strain / longitudinal strain.
Since we have different form of strain in the above equation and Dimensional Formula of Strain = M0L0T0.
And we know that ratio of dimensionless quantity is Dimensionless.
Therefore, Poisson’s ratio is Dimensionless and has no SI unit.