Unit Hydrograph Calculator

This calculator implements the SCS (now NRCS) dimensionless triangular unit hydrograph, a standard watershed-hydrology method for estimating how a drainage basin responds to a pulse of excess rainfall, documented in the agency's Technical Release 55 (TR-55, "Urban Hydrology for Small Watersheds," 2nd ed., 1986) alongside the broader National Engineering Handbook hydrology guidance. Time to Peak (Tp) is half the storm duration plus Basin Lag Time (Tp = D/2 + Tlag), and Peak Discharge (Qp) follows the metric form of the method's governing equation, Qp = 2.08 x A / Tp, where the 2.08 constant is the metric peak- rate factor equivalent to the customary-unit factor of 484 (a factor derived from the triangular hydrograph's assumed shape — roughly 3/8 of total runoff volume on the rising limb and 5/8 on the recession limb). From there, Time Base is 2.67 times Time to Peak and Time of Concentration is 1.67 times Basin Lag Time, both standard SCS shape relationships (the 2.67 and 1.67 factors both fall out of the same rising/recession-limb split).

Peak Discharge is expressed per centimeter of excess rainfall — the 2.08 metric peak-rate factor is calibrated to 1 cm of excess rainfall, not 1 mm, so Peak Discharge and Unit Volume should be read accordingly (Unit Volume, computed from Peak Discharge and Time Base, comes out close to Expected Volume (1cm), which is Drainage Area's own 1 cm-depth volume — that agreement is the built-in self-check that the unit convention is being applied consistently). Drainage Area is a direct multiplier into Peak Discharge with no offsetting term, while Basin Lag Time works in the opposite direction — a longer lag stretches Time to Peak and thereby lowers Peak Discharge, since the same rainfall volume is spread over more time. This is a standard textbook method assuming a single dimensionless triangular shape; real hydrographs from ungauged basins are commonly estimated this way as a starting point, then calibrated against observed gauge data where available — the peak-rate factor itself is documented to range from roughly 600 in steep terrain down to 100 or less in flat basins, well outside the fixed 2.08 (484) this calculator uses.