<p>Equations for the distribution of age versus length of partially annealed horizontal fission tracks in apatite is presented. Probabilistic least–squares inversion corrects natural track length histograms for observational biases considering the variance of data, modelization, and prior information. The corrected histogram is validated by its variance–covariance matrix. It is considered that horizontal track data can be with or without measurements of angles to the c–axis. In the last case, 3D–histograms are introduced as an alternative to histograms of c–axis projected track lengths. Thermal history modeling of samples is not necessary for track age distribution calculation. In an example the age equations are applied to apatites with pre–depositional (inherited) tracks, to extract the post–depositional track length histogram. Fission tracks generated before deposition in detrital apatite crystals are mixed with post–depositional tracks. This complicates the calculation of the post– sedimentary thermal history as the grains have experienced different thermal histories until deposition. Thereafter the grains share a common thermal history. The extracted post–depositional histogram without inherited tracks may be used for thermal history calculation.</p>