This paper presents an accurate estimation formula for the, minimum filter length of optimum (the minimax criterion based) FIR low-pass digital filters. The authors have proposed an accurate estimation formula for the particular case that the passband and stopband ripples are identical. Now we expand the formula for the general case. The accuracy of the proposed for mula is evaluated in comparison with that of the conventional formulae. It is also described how to apply the proposed-formula for the design of other types of filters.