Estimate the peak stormwater runoff rate from a small catchment with the rational method, Q = C·i·A. This calculator uses the SI form (Q in m³/s with rainfall intensity in mm/hr and area in hectares) and validates that the runoff coefficient C stays within its physical range of 0 to 1.
The rational method is the most widely used technique for estimating the peak stormwater discharge from small urban and rural catchments. It underpins the sizing of storm sewers, inlets, culverts, gutters, and small detention facilities. Its appeal is simplicity: a single equation, Q = C·i·A, ties peak flow to land cover, rainfall intensity, and area. This calculator implements the SI form and flags any runoff coefficient outside its valid 0-to-1 range.
Q = C · i · A / 360, where Q is the peak runoff (m³/s), C is the dimensionless runoff coefficient, i is the average rainfall intensity (mm/hr), and A is the catchment area (hectares). The factor 360 reconciles the units (mm/hr × ha → m³/s). In US-customary form the equation is Q = C·i·A with Q in cubic feet per second (cfs), i in inches per hour, and A in acres — there the unit-conversion constant is 1.008 and is conventionally taken as 1.
C is the fraction of rainfall that becomes surface runoff rather than infiltrating, evaporating, or being stored. It ranges from near 0 (highly permeable, flat, vegetated ground) to near 1 (impervious surfaces). Typical values: business/downtown 0.70–0.95, paved asphalt or concrete 0.80–0.95, roofs 0.75–0.95, residential (single-family) 0.30–0.50, lawns on heavy soil 0.18–0.35, lawns on sandy soil 0.05–0.20, parks and woodland 0.10–0.30. For mixed catchments use an area-weighted composite C. Because C must be a fraction, this calculator rejects values above 1.
The intensity i is not arbitrary — it is read from an Intensity-Duration-Frequency (IDF) curve for the design storm's return period (e.g. 10-year, 100-year). The crucial assumption is that the storm duration equals the catchment's time of concentration (t_c) — the time for runoff to travel from the hydraulically most remote point to the outlet. At that duration the whole catchment is contributing and the discharge peaks. Compute t_c first (using e.g. the Kirpich or TR-55 methods), then enter the IDF curve at that duration for the chosen frequency to get i.
The method assumes rainfall is uniform in space and time over the catchment, that the peak runoff coincides with the time of concentration, and that C is constant for a given surface. These assumptions break down for large or complex watersheds, so the rational method is generally limited to areas under about 80 hectares (200 acres); some agencies cap it lower. For larger catchments, routing-based or unit-hydrograph methods (such as SCS/NRCS TR-55 or TR-20) are used instead.
It converts the mixed input units to a consistent result. With i in mm/hr and A in hectares, C·i·A has units of mm·ha/hr; dividing by 360 yields m³/s (since 1 mm over 1 ha is 10 m³, and there are 3600 seconds per hour, giving 10/3600 = 1/360). Using the constant lets engineers keep the convenient field units of mm/hr and hectares.
Match C to the land cover, slope, and soil from a standard table, then area-weight the values across the catchment to get a composite C. Choose toward the higher end for steep slopes, compacted or wet antecedent soils, and severe (long return-period) storms, since infiltration capacity is relatively smaller during extreme events. Local drainage manuals usually prescribe the values to use.
Use the intensity from the IDF curve for your design return period evaluated at a duration equal to the catchment's time of concentration. That pairing represents the critical storm that produces the peak flow. Do not use a daily or hourly total — the rational method needs the average intensity over the concentration time, which for small urban areas is often only 5–20 minutes and therefore quite high.
It assumes spatially and temporally uniform rainfall and a single time of concentration. Over large watersheds rainfall varies, storage and channel routing attenuate the peak, and partial-area effects matter — so a single Q = C·i·A overestimates or misrepresents the response. Most agencies therefore restrict it to catchments under about 80 ha and switch to hydrograph or routing methods for larger basins.
The basic rational method gives only the single peak discharge — it is not a full hydrograph. A variant, the modified rational method, builds a simple trapezoidal or triangular hydrograph by varying the storm duration, which is useful for sizing detention storage. For a complete runoff hydrograph you generally move to unit-hydrograph or continuous-simulation models.