In the kinetic energy formula E = 1/2 mv², the numerical factor 1/2 is dimensionless and does not influence the dimensional analysis, which focuses on basic dimensions like length, mass, and time. Dimensional analysis can show relationships between formulas but cannot calculate numerical factors, requiring more advanced methods for such evaluations. The dimensional formula for energy is E = ML²T⁻², which does not differentiate between kinetic and potential energy. Additionally, dimensional analysis treats energy density and pressure similarly, despite their different physical meanings. Thus, while dimensional analysis is useful, it has limitations in establishing strict equivalence between different formulas.