The total mass budget of the Antarctic ice sheet is studied with a simple axi-symmetrical model. The ice-sheet has a parabolic profile resting on a bed that slopes linearly downwards from the centre of the ice sheet into the ocean. The mean ice velocity at the grounding line is assumed to be proportional to the water depth. The accumulation rate is a linear function of the distance to the centre. Setting the total mass budget to zero yields a quadratic equation for the steady-state ice-sheet radius R. Analysis of the equilibrium states sheds light on the sensitivity of the ice-sheet radius to changes in sea level (S) and precipitation with respect to the present state (Prel). For model parameters obtained by matching the analytical model to the present state of the Antarctic ice sheet, the sensitivity values are dR/dS = -2400 and dR/dPrel = 4000 m/%. The model can also be used to study transient behaviour of the ice sheet. The characteristic relaxation time (e-folding time scale) is about 3500 years. Forcing the model with a sea-level and accumulation history over the past few hundred thousands of years yields Antarctic ice-volume curves that are similar to those obtained by comprehensive numerical modelling. The current imbalance predicted by the model corresponds to a sea-level rise of 0.25 mm yr-1.