This paper presents an efficient numerical sensitivity-estimation method and implementation for continuous-gravitational-wave searches, extending and generalizing an earlier analytic approach by Wette [1]. This estimation framework applies to a broad class of F-statistic-based search methods, namely (i) semi-coherent StackSlide F-statistic (single-stage and hierarchical multistage), (ii) Hough number count on F-statistics, as well as (iii) Bayesian upper limits on F-statistic search results (coherent or semi-coherent). We test this estimate against results from Monte-Carlo simulations assuming Gaussian noise. We find the agreement to be within a few % at high detection (i.e., low false-alarm) thresholds, with increasing deviations at decreasing detection (i.e., higher false-alarm) thresholds, which can be understood in terms of the approximations used in the estimate. We also provide an extensive summary of sensitivity depths achieved in past continuous-gravitational-wave searches (derived from the published upper limits). For the F-statistic-based searches where our sensitivity estimate is applicable, we find an average relative deviation to the published upper limits of less than 10%, which in most cases includes systematic uncertainty about the noise-floor estimate used in the published upper limits.