We present the error budget of an astronomical single conjugated adaptive optics system with a pyramid wavefront sensor. The chosen approach is semianalytical to take into account the full response characteristics of this kind of sensor, and, in addition to these characteristics, it includes the closed-loop dynamics and all the main error sources: fitting, temporal, measurement, and aliasing error. This error budget has been made to complement more complex numerical simulators in the system design process, to rapidly explore a huge range of system parameters and to assess the critical components. Its reliability is demonstrated with a comparison with Monte Carlo numerical simulations on a reference system, the Single Conjugated Adaptive Optics Upgrade for Large Binocular Telescope.