Abstract: In order to calculate the maximum instantaneous dam-break discharge, a relationship between the maximum instantaneous dam-break discharge and the weir flow is established. The theory of equality of wave discharge and weir flow is applied in the study. A new generalized formula set is derived, which includes a basic formula, an up-limit formula, a low-limit formula and a generalized formula, etc. The verification results show that the new generalized formula set is capable of dealing with all types of breaches including whole dam collapse, horizontal partial dam-break, vertical partial dam-break, and both horizontal and vertical partial dam-break. The instantaneous dam-break discharge can be associated with the type of weirs. The new generalized formula set integrates equations for the instantaneous dam-break discharge, and the overtopping or gradually dam-break flood flow, as well as the corresponding coefficients into weir formulas. The values of the coefficients are reliable as they have been validated by available experimental data and classic scientific works. The new generalized formula set is validated with dam-break flow experiments and real-case data, and is proven to be rational and reliable.