Chromosomal instability (CIN) drives the formation of karyotype aberrations in cancer cells and is a major contributor to intra-tumour heterogeneity, metastasis, and therapy resistance. Understanding how CIN contributes to tumour karyotype evolution requires quantification of CIN rates in primary tumours. Single-cell sequencing-based technologies enable the detection of karyotype heterogeneity, however deducing the actual CIN rates that underlie intra-tumour heterogeneity is still complicated. We have developed an in-silico model, called CINsim, to simulate the karyotype dynamics and validated our model in a murine mouse model for T-cell lymphoma (T-ALL) in which CIN is introduced by mutation of the Mps1 spindle assembly checkpoint protein. CINsim can simulate karyotype evolution within physiologically relevant timescales, across a range of CIN rates, and across a range of karyotype-imposed survival and proliferation effects. We find that CINsim can accurately predict the CIN rates in chromosomal instable mouse T-ALLs as well as in human colon cancer organoids as observed by live-cell time-lapse imaging. We conclude that CINsim is a powerful tool to estimate CIN rates from static single-cell DNA sequencing data by finding the most likely path from euploid founder cell to a heterogeneous tumour cell population.