This paper describes the use of analytical methods to determine machinable centrifugal impeller geometries and the use of computational fluid dynamics for predicting impeller performance. An analytical scheme is described to determine machinable geometries for a shrouded centrifugal impeller with blades composed of equiangular spirals. The scheme is used to determine the maximum machinable blade angles for impellers with 3 to 9 blades in a case study. Computational fluid dynamics is then used to analyse all machinable geometries and determine the optimal blade number and angle based on measures of efficiency, rotor speed, blade shear stress and eddy viscosity. The effect of tip width on rotor speed and efficiency is also examined. It is found that, for our case study, a six or seven bladed impeller with a low blade angle provides maximum efficiency and minimum hemolysis.