Cutaneous squamous cell cancers (cSCCs) present an under-recognized health issue among non-Hispanic whites, one that is likely to increase as populations age. cSCC risks vary considerably among non-Hispanic whites, and this heterogeneity indicates the need for risk-stratified screening strategies that are guided by patients' personal characteristics and clinical histories. Here we describe cSCCscore, a prediction tool that uses patients' covariates and clinical histories to assign them personal probabilities of developing cSCCs within 3 years after risk assessment. cSCCscore uses a statistical model for the occurrence and timing of a patient's cSCCs, whose parameters we estimated using cohort data from 66,995 patients in the Kaiser Permanente Northern California healthcare system. We found that patients' covariates and histories explained approximately 75% of their interpersonal cSCC risk variation. Using cross-validated performance measures, we also found cSCCscore's predictions to be moderately well calibrated to the patients' observed cSCC incidence. Moreover, cSCCscore discriminated well between patients who subsequently did and did not develop a new primary cSCC within 3 years after risk assignment, with area under the receiver operating characteristic curve of approximately 85%. Thus, cSCCscore can facilitate more informed management of non-Hispanic white patients at cSCC risk. cSCCscore's predictions are available at https://researchapps.github.io/cSCCscore/.