Non-coding RNAs (ncRNA) are essential for all life, and their functions often depend on their secondary (2D) and tertiary structure. Despite the abundance of software for the visualisation of ncRNAs, few automatically generate consistent and recognisable 2D layouts, which makes it challenging for users to construct, compare and analyse structures. Here, we present R2DT, a method for predicting and visualising a wide range of RNA structures in standardised layouts. R2DT is based on a library of 3,647 templates representing the majority of known structured RNAs. R2DT has been applied to ncRNA sequences from the RNAcentral database and produced >13 million diagrams, creating the world's largest RNA 2D structure dataset. The software is amenable to community expansion, and is freely available at https://github.com/rnacentral/R2DT and a web server is found at https://rnacentral.org/r2dt .