New radiative data for allowed and forbidden transitions between the 3s23p2, 3s3p3 and 3s23p3d configurations of Fe XIII are presented. The calculations are performed with the SSTRUCT atomic code, including 24 configurations in the model, and term energy corrections have been applied to optimise the theoretical level energies. The new data-set is compared with other calculations in the literature and also an unpublished calculation of Young that is found in the CHIANTI atomic database. Good agreement is found in all cases except with calculations of Nahar. Comparisons are also presented with laboratory and solar experimental data that demonstrate the accuracy of the present calculations. The new data are to be added to version 5 of the CHIANTI atomic database.