Abstract: The calculation of the minimum emittance of three-bend achromats (TBAs) made by Mathematica software can ignore the actual magnets lattice in the matching condition of dispersion function in phase space. The minimum scaling factors of two kinds of widely used TBA lattices are obtained. Then the relationship between the lengths and the radii of the three dipoles in TBA is obtained and so is the minimum scaling factor, when the TBA lattice achieves its minimum emittance. The procedure of analysis and the results can be widely used in achromats lattices, because the calculation is not restricted by the actual lattice.