AbstractWithin a normal operating range of extruders, it has been well established that the output increases nearly proportionally to the screw speed but the screw horsepower increases more than proportionally to the screw speed, making the screw HP difficult to predict. It has been also known in scale‐up of extruders that the output may be predicted with reasonable accuracy but the screw HP is difficult to predict. No sound theoretical or empirical method predicting screw HP in a scale‐up calculation has been offered heretofore. Since a screw performs solid conveying, melting and pumping (or metering) functions simultaneously, any theoretical analysis of screw HP has to consider all three extrusion theories; solid conveying theory, melting theory and pumping theory. In this paper, semi‐theoretical equations for predicting screw HP as a function of screw speed and size are developed. Experiments are conducted to test the utility of these equations and the implications of the experimental results on extrusion theories are disc