Radio astronomy file formats are now required to store wide frequency bandwidths and multiple simultaneous receiver beams and must be able to account for versatile observing modes and numerous calibration strategies. The need to capture and archive high-time and high frequency-resolution data, along with the comprehensive metadata that fully describe the data, implies that a new data format and new processing software are required. This requirement is suited to a well-defined, hierarchically-structured and flexible file format. In this paper we present the Spectral-Domain Hierarchical Data Format (‘SDHDF’) — a new file format for radio astronomy data, in particular for single dish or beam-formed data streams. Since 2018, SDHDF has been the primary format for data products from the spectral-line and continuum observing modes at Murriyang, the CSIRO Parkes 64-metre radio telescope, and we demonstrate that this data format can also be used to store observations of pulsars and fast radio bursts.