The scalar-product formula of the excess free energy σ of a boundary between two phases (based on the lattice model) is proved for the case of interaction potential of the range longer than the nearest neighbor. The formula is exp(−Aσ/kT) =Σ[p(I)(ν1,ν2,...,νk) p(II)(ν1,ν2,...,νk)]1/2 exp[α(I)(ν1,ν2,...,νk)− α(II)(ν1,ν2,...,νk)], where A is the sectional area parallel to the boundary, νi is a configuration of an ith plane parallel to the boundary, p(I)(ν1,...,νk) is the probability that k consecutive planes in the bulk I phase take configurations ν1,...,νk, and the summation goes over all configurations ν1,...,νk. The variable α(I)(ν1,ν2,...,νk) is a Lagrange multiplier to guarantee continuity of p(I): Σμp(I)(μ,ν1,ν2,...,νk) = Σμp(I)(ν1,ν2,...,νk,μ). The expression is checked by two examples. The σ for the two-dimensional Ising model is calculated using a 3×2 cluster (i.e., a double square cluster made of six lattice points) with the ’’3’’-side perpendicular to the boundary, and is compared with the previous σ calculated with a 2×3 cluster (with the ’’3’’-side parallel to the boundary). The calculated σ’s agree well when the α terms are included. As a second example, surface tension σ of a liquid of a two-dimensional lattice gas–liquid model (in which the first, second, and third neighbor pairs are excluded, and the fourth and fifth neighbor pairs attract) is calculated. It is then compared with σ calculated by a sum method (which calculates the equilibrium state of a sandwich system made of the gas and the liquid phases with the boundary between them). The agreement between the two calculations supports the correctness of the proposed σ expression.