The higher magnetic levitation force and related stiffness values are very important for Maglev and magnetic bearing applications. Also, larger superconducting surface area is needed for continuous and larger magnetic mediums with different geometries and dimensions in real scale industrial applications of superconducting systems. In this study, the cylindrical YBCO superconductors were fabricated by top-seeded melt growth (TSMG) method in single and two-seeded forms with different seed distances and then the magnetic force and stiffness measurements were carried out by three axes magnetic force measurement system in different cooling heights (CH) of 20mm and 75 mm. Additionally, a new analytical method, based on the magnetic dipole approximation, is proposed to calculate the levitation force in this study, named as Modified Advanced Frozen Image Method (MAFI), since although the Advanced Frozen Image Method in literature can calculate the levitation force with hysteresis, this method does not include the size effect of the superconductor. In the experimental studies, it is seen that the maximum levitation force values obtained by PMG with three PMs (named PMG-1) are more than two times higher than that of obtained with single PM for all samples with different distance of seeds, because of the higher magnetic flux distribution of related PMG arrangement than the single PM. In addition, the maximum magnetic levitation force value firstly increased and then decreased due to current coupling effect weakness by increasing distance of seeds. The calculated analytical levitation force results are not compatible with the experimental results without current coupling effect, but a well agreement is observed when the current coupling effect is taken into account in calculations. Also the MAFI method was tested with different dimensions of superconductors and the obtained results indicated the success of the proposed method. The maximum levitation force values obtained with MAFI method increased with increasing dimensions of HTS and PMs. Thus, one can say that the MAFI method is useful for the levitation force calculations between multi-seeded superconductors and PMGs with different dimensions and for different CHs. As a result, the analytical levitation force values obtained with the MAFI method are agree with the experimental levitation force sufficiently and this method can give fast calculation results without any divergence problem. This method can be thought as an alternative to the numerical calculation methods, having serious divergence problems for much amount and bigger size superconducting samples, therefore it will be useful to clarify bulk superconducting properties as supporter to the experimental studies. (C) 2019 Elsevier B.V. All rights reserved.