Altered centrosome numbers are seen in tumor cells in response to DNA damaging treatments and are hypothesised to contribute to cancer development. The mechanism by which the centrosome and chromosome cycles become disconnected after DNA damage is not yet clear. Here, we show that centrosome amplification occurs after ionising radiation (IR) in chicken DT40 cells that lack DNA-PK, Ku70, H2AX, Xpa, and Scc1, demonstrating that these activities are not required for centrosome amplification. We show that inhibition of topoisomerase II induces Chk1-dependent centrosome amplification, a similar response to that seen after IR. In the immortalised, nontransformed hTERT-RPE1 line, we observed centriole splitting, followed by dose-dependent centrosome amplification, after IR. We found that IR results in the formation of single, not multiple, daughter centrioles during centrosome amplification in U2OS osteosarcoma cells. Analysis of BRCA1 and BRCA2 mutant tumor cells showed high levels of centriole splitting in the absence of any treatment. IR caused pronounced levels of centrosome amplification in BRCA1 mutant breast cancer cells. These data show that centrosome amplification occurs after different forms of DNA damage in chicken cells, in nontransformed human cells and in human tumor cell lines, indicating that this is a general response to DNA damaging treatments. Together, our data suggest that centriole splitting is a key step in potentiation of the centrosome amplification that is a general response to DNA damage.