Model approaches to nuclear architecture have traditionally ignored the biophysical consequences of ATP-fueled active processes acting on chromatin. However, transcription-coupled activity is a source of stochastic forces that are substantially larger than the Brownian forces present at physiological temperatures. Here, we describe a first-principles approach to large-scale nuclear architecture in metazoans that incorporates cell-type-specific active processes. The model predicts the statistics of positional distributions, shapes and overlaps of each chromosome. Our simulations reproduce common organising principles underlying large-scale nuclear architecture across human cell nuclei in interphase. These include the differential positioning of euchromatin and heterochromatin, the territorial organisation of chromosomes including both gene-density-based and size-based chromosome radial positioning schemes, the non-random locations of chromosome territories and the shape statistics of individual chromosomes. We propose that the biophysical consequences of the distribution of transcriptional activity across chromosomes should be central to any chromosome positioning code.