AbstractThis paper defines the mathematical convention adopted to describe an electromagnetic wave and its polarisation state, as implemented in the psrchive software and represented in the psrfits definition. Contrast is made between the convention that has been widely accepted by pulsar astronomers and the IAU/IEEE definitions of the Stokes parameters. The former is adopted as the PSR/IEEE convention, and a set of useful parameters are presented for describing the differences between the PSR/IEEE standard and the conventions (either implicit or explicit) that form part of the design of observatory instrumentation. To aid in the empirical determination of instrumental convention parameters, well-calibrated average polarisation profiles of PSR J0304+1932 and PSR J0742–2822 are presented at radio wavelengths of approximately 10, 20, and 40 cm.