Tsunami risk reduction activities rely on a sound knowledge of the hazard characteristics. Our understanding of these characteristics is derived from empirical measurements, numerical models or established rules. Conventional methods used to delineate areas vulnerable to tsunami inundation are often calculated from estimated maximum wave height at the coast and “rules-of-thumb”. Applying such rules may give unreliable results for decision-makers. Using basic hydraulic principles and assumptions, this paper improves on the existing rules by developing and testing new equations for predicting tsunami maximum depth profiles and inundation distances. The proposed equations require knowledge of shoreline wave-crest level, the onshore ground profile and an index for onshore roughness (a ratio of distance between protrusions to a local friction factor). As a tsunami wave moves inland, the equations demonstrate that there will usually be an exponential decline in peak water depth. The equations also confirm that a smaller spacing between onshore roughness elements, such as trees or houses, will give a steeper decline in peak depth due to increased friction as a wave moves inland. Furthermore, where ground level is rising faster than friction head is being lost, it is predicted that the water level of a tsunami will rise above the shoreline wave-crest level. The ground slope at which run-up starts to exceed shoreline wave-crest level can be predicted from the shoreline wave-crest level and roughness spacing. Results predicted by the new equations are verified by comparison with tsunami run-up measurements made in Samoa and Java.