Context. Large-scale coronal waves, also referred to as extreme-ultraviolet (EUV) waves, are a common phenomenon of solar activity in the Sun’s corona. They are observed in EUV light as global waves travelling over one hemisphere of the Sun. Previous studies of EUV waves defined three classes based on their kinematical properties. In particular, class 1 waves show a decrease in velocity during their evolution over the solar surface. These special EUV waves are considered as the manifestation of large-amplitude magnetohydrodynamic (MHD) waves in the corona. Aims. We use a sample of seven class 1 EUV waves observed by the EUVI instruments onboard the two STEREO spacecraft to derive the relationship between the initial velocity and deceleration. This relationship can be explained in terms of the theory of large-amplitude MHD waves. Methods. We employ non-linear MHD equations to describe large-amplitude, fast magnetosonic waves in terms of so-called ‘simple MHD waves’. Results. The theory of simple MHD waves provides a relationship between the initial velocity and deceleration of the wave. The observations agree well with the non-linear evolution of a spherical large-amplitude, fast magnetosonic wave. Conclusions. The kinematical properties of large-scale EUV waves can be well described by the theory of large-amplitude (simple) MHD waves.