A key goal in the study of the function of ATP-driven motor enzymes is to quantify the movement produced from consumption of one ATP molecule. Discrete displacements of the processive motor kinesin along a microtubule have been reported as 5 and/or 8 nm. However, analysis of nanometre-scale movements is hindered by superimposed brownian motion. Moreover, because kinesin is processive and turns over stochastically, some observed displacements must arise from summation of smaller movements that are too closely spaced in time to be resolved. To address both of these problems, we used light microscopy instrumentation with low positional drift (< 39 pms[-1]) to observe single molecules of a kinesin derivative moving slowly (approximately 2.5nm s[-1]) at very low (150nM) ATP concentration, so that ATP-induced displacements were widely spaced in time. This allowed increased time-averaging to suppress brownian noise (without application of external force), permitting objective measurement of the distribution of all observed displacement sizes. The distribution was analysed with a statistics-based method which explicitly takes into account the occurrence of unresolved movements, and determines both the underlying step size and the coupling of steps to ATP hydrolytic events. Our data support a fundamental enzymatic cycle for kinesin in which hydrolysis of a single ATP molecule is coupled to a step distance of the microtubule protofilament lattice spacing of 8.12 nm. Step distances other than 8nm are excluded, as is the coupling of each step to two or more consecutive ATP hydrolysis reactions with similar rates, or the coupling of two 8-nm steps to a single hydrolysis. The measured ratio of ATP consumption rate to stepping rate is invariant over a wide range of ATP concentration, suggesting that the 1 ATP to 8nm coupling inferred from behaviour at low ATP can be generalized to high ATP.