Young's equation (${\gamma }_{SV}={\gamma }_{SL}+{\gamma }_{LV}\cos \theta$)

For a smooth homogeneous solid in thermodynamic equilibrium with a liquid and vapor, Young's equation relates their three interfacial tensions to the contact angle measured through the liquid. A virtual increase $dA$ of wetted area changes the interfacial free energy by $({\gamma }_{SL}-{\gamma }_{SV}+{\gamma }_{LV}\cos \theta )dA$. Setting this to zero proves the equation. Roughness, pinning and chemical heterogeneity can make an observed apparent angle differ from this ideal equilibrium value. The equation does not determine each solid–liquid surface energy from a contact angle alone, but two liquids on the same unchanged dry substrate allow the solid–vapor term to be eliminated by subtraction.