This dataset contains the sea-level fields for the new Kalman Smoother reconstruction submitted for publication under the title as "Probabilistic reconstruction of sea-level changes and their causes since 1900" by Soenke Dangendorf, Qiang Sun, Thomas Wahl, Philip Thompson, Jerry X. Mitrovica, and Ben Hamlington. The dataset contains the fields of total sea level and individual components (KSSLfin.mat) and their errors (KSSL_SEfin.mat). Master_Final.m is the master MATLAB script that performs the analysis of the data and also contains an explainer of main acronyms. Please note that you need the m_map toolbox to perform most of the plots (https://www.eoas.ubc.ca/~rich/map.html). All other sub-functions have been added, e.g., the Singular Spectrum Analysis originally published and written by Aslak Grinsted (Moore, J. C., Grinsted, A., & Jevrejeva, S. (2005). New tools for analyzing time series relationships and trends. Eos, Transactions American Geophysical Union, 86(24), 226-232). Also included are datasets from the following publications: Camargo, C. M., Riva, R. E., Hermans, T. H., & Slangen, A. B. (2020). Exploring sources of uncertainty in steric sea‐level change estimates. Journal of Geophysical Research: Oceans, 125(10), e2020JC016551. Frederikse, T., Landerer, F., Caron, L., Adhikari, S., Parkes, D., Humphrey, V. W., ... & Wu, Y. H. (2020). The causes of sea-level rise since 1900. Nature, 584(7821), 393-397. Palmer, M. D., Domingues, C. M., Slangen, A. B. A., & Dias, F. B. (2021). An ensemble approach to quantify global mean sea-level rise over the 20th century from tide gauge reconstructions. Environmental Research Letters, 16(4), 044043. WCRP(2018). Global sea-level budget 1993--present. Earth System Science Data, 10(3), 1551-1590.