The algebraic relationships between friction force F and normal force N on the rake face of a tool, and between average stress distributions qF and qN, are derived for an assumed power law stress distribution of the normal contact pressure p between chip and rake face, i.e. for p=po(x/L)n, as used by Zorev, where x is measured towards the tip of the tool from an origin at the end of the contact region of length L, and po is the maximum pressure at the cutting edge. The derived expressions suggest a novel method of determining quantitatively the lengths s of stuck regions on the rake face, and unstuck lengths (L–s), just from the cutting forces without the use of special devices such as split tooling. Calculations for the variations of (s/L) and μapparent=qF/qN with uncut chip thickness t automatically give the variation in values of po and n. The theory is tested using experimental cutting force data in the literature from a wide range of materials in different thermomechanical states and the predictions are compared with independent data. It is demonstrated that the usually-illustrated version of the Zorev pressure distribution where the contact pressure rises ‘exponentially’ to the cutting edge (i.e. where n>1) applies only when (s/L) is less than about 0.5. When the sticking length s is a larger proportion of L, n<1 giving the experimentally-known different type of pressure distribution that levels out towards the cutting edge.Theory and experiments show that qF plots non-linearly against qN for all combinations of uncut chip thickness t and rake face contact length L. The plot emanates from the origin with an initial slope of μCoulomb. As soon as the sticking length s begins to increase, the slope diminishes and when (s/L)=1 at complete sticking, the local slope of the qF vs qN is zero. Increasing (s/L) corresponds to a reduction in (L/t) that may be achieved using restricted contact tools, but even in full-face cutting where L=Lff there is some sticking near the cutting edge at the largest (Lff/t).Plots of friction force F vs normal force N along the rake face are also predicted to be non-linear and emanate from the origin with slope μCoulomb. While some experimental results display this shape, most F vs N experimental data for full-face cutting follow linear “F=Fo+ϖN” relations (having high correlation coefficients). It is shown that such linear plots with intercepts are tangents to the more general non-linear relations, and are caused by the relatively small range of qF and qN encountered in full-face cutting which is caused by the interplay between rates of increase of cutting forces as t increases, and rates of change of Lff/t with increasing t. How (s/L), po and n may be determined from such plots without knowledge of μCoulomb is explained and calculations from experiments are made.The loads expected to be measured by split tools having a Zorev contact pressure distribution are also predicted and compare favourably with experiment.