SCS Curve Number runoff · Triangular unit hydrograph · Peak flow & timing
This simulator generates a stormwater runoff hydrograph using the NRCS (SCS) Curve Number method for runoff depth and the SCS dimensionless unit hydrograph for peak flow timing — the standard approach for detention pond design and FEMA floodplain studies on small to medium watersheds.
The NRCS method has two components. First, runoff depth Q (inches) is calculated from rainfall depth P (inches) and Curve Number CN: S = 1000/CN − 10 (inches), Ia = 0.2S (initial abstraction), and Q = (P − 0.2S)² / (P + 0.8S) for P > Ia, else Q = 0. The CN encodes soil type and land use, ranging from 30 (forested, well-drained soil) to 98 (impervious surfaces).
Second, the triangular unit hydrograph converts runoff depth to a flow hydrograph. Lag time tL = 0.6·Tc and time to peak Tp = D/2 + tL (D is the unit storm duration, typically 0.133·Tc for the dimensionless UH). Peak discharge Qp = 484 · A · Q / Tp, where A is in square miles and Q is in inches. Time base Tb = 8/3·Tp. The 484 peak rate factor is empirical and represents average watershed conditions; it may be adjusted to 300–600 for flatter or steeper terrain.
The SCS/NRCS method is documented in NRCS National Engineering Handbook Part 630 (Hydrology) and Technical Release 55 (TR-55). It is the required or preferred method in many state stormwater regulations and is built into HEC-HMS (USACE Hydrologic Modeling System), the industry-standard hydrologic modeling software. FEMA accepts TR-55 and HEC-HMS analyses for Flood Insurance Studies and Letters of Map Revision (LOMR). TR-20 uses the full dimensionless S-graph unit hydrograph rather than the simplified triangular approximation used here.
Curve Number selection is the most consequential input. Using the wrong CN by ±10 can change peak flow by 30–50%. CN values are tabulated in TR-55 Table 2-2 by land use and Hydrologic Soil Group (A through D). HSG is determined from NRCS Web Soil Survey or a geotechnical report. For mixed land cover, compute a composite CN weighted by sub-area.
Time of concentration Tc must be estimated carefully — TR-55 provides the sheet flow, shallow concentrated flow, and channel flow components that are summed to get total Tc. A 20% error in Tc produces approximately 10% error in peak discharge. The simulator uses D = 0.133·Tc (appropriate for the NRCS triangular unit hydrograph), consistent with TR-55 methodology.
Set the 24-hour design storm rainfall depth P (inches) — obtain from NOAA Atlas 14 for your location and storm frequency. Enter the composite Curve Number CN, drainage area A (acres), and time of concentration Tc (hours). The calculator displays runoff depth, peak flow Qp, time to peak Tp, time base Tb, and runoff volume, along with the triangular hydrograph. Use Qp as the inflow to the Detention Pond Routing Simulator to size your stormwater management facility.
The triangular unit hydrograph is a simplified approximation where the rising limb goes linearly from 0 to Qp over Tp, then falls linearly to 0 at Tb = 2.67·Tp. The full NRCS dimensionless unit hydrograph (S-graph) is a smooth, slightly skewed shape used in TR-20 and HEC-HMS. For most engineering applications the triangular UH provides results within 10–15% of the full UH and is preferred for hand calculations and preliminary design.
For 1/4-acre residential lots (approximately 38% impervious) with HSG B soil: CN = 75. HSG C: CN = 83. HSG D: CN = 87. For 1/8-acre lots (65% impervious) with HSG C: CN = 90. Always verify land use and soil group from NRCS Web Soil Survey and TR-55 Table 2-2 for your specific project.
Rainfall must exceed the initial abstraction Ia = 0.2S before any surface runoff occurs. Ia represents interception by vegetation, depression storage, and early infiltration. For CN = 70, S = 4.29 in and Ia = 0.86 in, so storms under about 0.9 inches produce zero runoff. For CN = 90, Ia = 0.22 in, so even small storms generate runoff — which is why high-CN (impervious) sites are much more sensitive to frequent small storms.
A shorter Tc means water reaches the outlet faster, resulting in a shorter, higher-peaked hydrograph. Doubling Tc roughly halves the peak discharge (Qp ∝ 1/Tp, Tp ∝ Tc). This is why site development that increases impervious cover and shortens flow paths — reducing Tc — dramatically increases peak flows even if the CN increase is modest.
The TR-55 triangular unit hydrograph is recommended for watersheds up to about 2000 acres (3 square miles). For larger watersheds, or watersheds with complex routing (reservoirs, diversions), use HEC-HMS with the full NRCS dimensionless unit hydrograph and a routing scheme such as Muskingum or level-pool routing for each sub-watershed.