We introduce a new parameter, tsunami runup predictor (TRP), relating the accelerating phase of the wave to the length of the beach slope over which the wave is travelling. We show the existence of a relationship between the TRP and the runup for different initial waveforms, i.e. leading elevation N-waves (LENs) and leading depression N-waves (LDNs). Then, we use the TRP to estimate tsunami runup for past tsunami events. The comparison of the runup estimates against field data gives promising results. Thus, the TRP provides first-order estimates of tsunami runup once the offshore waveform is known or estimated and, therefore, it could be beneficial to be implemented in tsunami early warning systems.