Volcanic radiative forcing reconstruction is an important part of paleoclimate simulation and attribution efforts, and the conversion factor used to transfer ice core-based sulfate observation into stratospheric volcanic aerosol loading (LTD factor) is critical for such reconstruction. A Pinatubo-based LTD was proposed and adapted in the CMIP5 and CMIP6 volcanic forcing, under the assumption that all tropical eruptions follow the same atmospheric transport and deposition pattern. This study revisits the LTD factor using a large collection of polar ice core records of Tambora deposition and a Monte Carlo sampling model. A new set of LTDs with associated uncertainties are obtained, which is in approximate with our previous Pinatubo-based LTD estimation in Greenland, while corrects the bias of over-representing the west Antarctic. The uncertainties revealed from the Monte Carlo simulation suggest that, difference in the ice core abundance only introduce limited uncertainty in LTD for individual eruption, once reach a certain threshold (about 15 in Greenland and 20 in Antarctic). The comparison of Southern Hemispheric LTD among Tambora, Agung, and Pinatubo suggests that, the conversion factor may vary for individual eruption. Results obtained from this study may ease our conventional proneness to use as much ice core observations as available to estimate icecap volcanic deposition, while emphasize the importance to build a distribution of the LTD ideally for eruptions with different size and locations. Meanwhile, the estimated sets of Tambora-based LTDs could serve as a compromising choice in future volcanic forcing reconstruction work, especially when Tambora is utilized as a reference