In statistical mechanics and thermodynamics the compressibility equation refers to an equation which relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid. It reads: k T ( ∂ ∂ ρ ρ ∂ ∂ p ) = 1 + ρ ρ ∫ ∫ V d r [ g ( r ) − − 1 ] where ρ ρ is the number density, g(r) is the radial distribution function and k T ( ∂ ∂ ρ ρ ∂ ∂ p ) is the isothermal compressibility.