Rational Method Calculator
Peak flow by the Rational Method, Q = CiA, with the rainfall intensity for your time of concentration from NOAA Atlas 14.
Results
Enter your values; the answer appears here as you type.
The curve appears with a result.
- The equation
- Q = C i A in US customary units: Q in cfs, i in in/hr and A in acres (the unit factor 1.008 is taken as 1, as FHWA HEC-22 and the TxDOT Hydraulic Design Manual do). With several subareas, C is weighted by area.
- Intensity from NOAA Atlas 14
- For a Texas location the intensity is the Atlas 14 depth for a duration equal to the time of concentration, divided by that duration. Between published durations the depth is interpolated on a log-log line. The duration can be held to a minimum of 10 minutes (TxDOT) or 5 minutes; Tc itself is reported unchanged.
- Every return period
- With a location, the peak for every return period from 1 to 1,000 years is listed and plotted for the same area, C and duration.
- No frequency factor
- HEC-22 (4th ed.) notes that some agencies multiply C by a frequency-of-event correction factor and that FHWA does not endorse it, so none is applied. Its C table notes that higher values in a range generally suit steep areas and less frequent storms.
- Assumptions
- Rain falls at a uniform intensity over the whole area for at least Tc; the peak occurs when the whole area contributes; storage is not significant. FHWA HDS-2 (cited in HEC-22) and the TxDOT Hydraulic Design Manual limit the method to about 200 acres; many local criteria set lower limits.
FHWA HEC-22 (4th ed., 2024) — Table 4.1, Runoff coefficients for the Rational Method (ASCE 1960)
| Surface or land use | C |
|---|---|
| Business: Downtown areas | 0.70–0.95 |
| Business: Neighborhood areas | 0.50–0.70 |
| Residential: Single-family areas | 0.30–0.50 |
| Residential: Multi-units, detached | 0.40–0.60 |
| Residential: Multi-units, attached | 0.60–0.75 |
| Residential: Suburban | 0.25–0.40 |
| Residential: Apartment dwelling areas | 0.50–0.70 |
| Industrial: Light areas | 0.50–0.80 |
| Industrial: Heavy areas | 0.60–0.90 |
| Open: Parks, cemeteries | 0.10–0.25 |
| Open: Playgrounds | 0.20–0.40 |
| Open: Railroad yard areas | 0.20–0.40 |
| Open: Unimproved areas | 0.10–0.30 |
| Lawns: Sandy soil, flat, 2% | 0.05–0.10 |
| Lawns: Sandy soil, average, 2 - 7% | 0.10–0.15 |
| Lawns: Sandy soil, steep, 7% | 0.15–0.20 |
| Lawns: Heavy soil, flat, 2% | 0.13–0.17 |
| Lawns: Heavy soil, average, 2 - 7% | 0.18–0.22 |
| Lawns: Heavy soil, steep, 7% | 0.25–0.35 |
| Streets: Asphaltic | 0.70–0.95 |
| Streets: Concrete | 0.80–0.95 |
| Streets: Brick | 0.70–0.85 |
| Other impervious: Drives and walks | 0.75–0.85 |
| Other impervious: Roofs | 0.75–0.95 |
FHWA, Urban Drainage Design Manual, HEC-22, 4th ed., FHWA-HIF-24-006, 2024, Table 4.1 (values from ASCE 1960). Higher values are generally appropriate for steeply sloped areas and less frequent AEPs because infiltration and other losses have a proportionally smaller effect on runoff in these cases (table footnote).
TxDOT HDM Ch. 4 (2019) — Table 4-10, Runoff coefficients for urban watersheds
| Surface or land use | C |
|---|---|
| Business: Downtown areas | 0.70–0.95 |
| Business: Neighborhood areas | 0.30–0.70 |
| Residential: Single-family areas | 0.30–0.50 |
| Residential: Multi-units, detached | 0.40–0.60 |
| Residential: Multi-units, attached | 0.60–0.75 |
| Residential: Suburban | 0.35–0.40 |
| Residential: Apartment dwelling areas | 0.30–0.70 |
| Industrial: Light areas | 0.30–0.80 |
| Industrial: Heavy areas | 0.60–0.90 |
| Other areas: Parks, cemeteries | 0.10–0.25 |
| Other areas: Playgrounds | 0.30–0.40 |
| Other areas: Railroad yards | 0.30–0.40 |
| Unimproved areas: Sand or sandy loam soil, 0-3% | 0.15–0.20 |
| Unimproved areas: Sand or sandy loam soil, 3-5% | 0.20–0.25 |
| Unimproved areas: Black or loessial soil, 0-3% | 0.18–0.25 |
| Unimproved areas: Black or loessial soil, 3-5% | 0.25–0.30 |
| Unimproved areas: Black or loessial soil, > 5% | 0.70–0.80 |
| Unimproved areas: Deep sand area | 0.05–0.15 |
| Unimproved areas: Steep grassed slopes | 0.70 |
| Lawns: Sandy soil, flat 2% | 0.05–0.10 |
| Lawns: Sandy soil, average 2-7% | 0.10–0.15 |
| Lawns: Sandy soil, steep 7% | 0.15–0.20 |
| Lawns: Heavy soil, flat 2% | 0.13–0.17 |
| Lawns: Heavy soil, average 2-7% | 0.18–0.22 |
| Lawns: Heavy soil, steep 7% | 0.25–0.35 |
| Streets: Asphaltic | 0.85–0.95 |
| Streets: Concrete | 0.90–0.95 |
| Streets: Brick | 0.70–0.85 |
| Other impervious: Drives and walks | 0.75–0.95 |
| Other impervious: Roofs | 0.75–0.95 |
Texas Department of Transportation, Hydraulic Design Manual, Chapter 4 Hydrology, Section 12 Rational Method, Table 4-10 (Manual Notice 2019-1). TxDOT: the table suggests ranges of C for various combinations of land use and soil or surface type and is typical of civil engineering design guides.
TxDOT HDM Ch. 4 (2019) — Table 4-11, Runoff coefficients for rural watersheds (C = Cr + Ci + Cv + Cs)
| Surface or land use | C |
|---|---|
| Relief, Cr: Extreme: steep, rugged terrain with average slopes above 30% | 0.28–0.35 |
| Relief, Cr: High: hilly, with average slopes of 10-30% | 0.20–0.28 |
| Relief, Cr: Normal: rolling, with average slopes of 5-10% | 0.14–0.20 |
| Relief, Cr: Low: relatively flat land, with average slopes of 0-5% | 0.08–0.14 |
| Soil infiltration, Ci: Extreme: no effective soil cover; either rock or thin soil mantle of negligible infiltration capacity | 0.12–0.16 |
| Soil infiltration, Ci: High: slow to take up water, clay or shallow loam soils of low infiltration capacity or poorly drained | 0.08–0.12 |
| Soil infiltration, Ci: Normal: well drained light or medium textured soils, sandy loams | 0.06–0.08 |
| Soil infiltration, Ci: Low: deep sand or other soil that takes up water readily; very light, well-drained soils | 0.04–0.06 |
| Vegetal cover, Cv: Extreme: no effective plant cover, bare or very sparse cover | 0.12–0.16 |
| Vegetal cover, Cv: High: poor to fair; clean cultivation, crops or poor natural cover, less than 20% of drainage area has good cover | 0.08–0.12 |
| Vegetal cover, Cv: Normal: fair to good; about 50% of area in good grassland or woodland, not more than 50% of area in cultivated crops | 0.06–0.08 |
| Vegetal cover, Cv: Low: good to excellent; about 90% of drainage area in good grassland, woodland, or equivalent cover | 0.04–0.06 |
| Surface storage, Cs: Extreme: negligible; surface depressions few and shallow, drainageways steep and small, no marshes | 0.10–0.12 |
| Surface storage, Cs: High: well-defined system of small drainageways, no ponds or marshes | 0.08–0.10 |
| Surface storage, Cs: Normal: considerable surface depression, e.g., storage lakes and ponds and marshes | 0.06–0.08 |
| Surface storage, Cs: Low: much surface storage, drainage system not sharply defined; large floodplain storage, large number of ponds or marshes | 0.04–0.06 |
Texas Department of Transportation, Hydraulic Design Manual, Chapter 4 Hydrology, Section 12 Rational Method, Table 4-11 and Equation 4-22 (Manual Notice 2019-1). For rural watersheds: pick one component each for relief, soil infiltration, vegetal cover and surface storage and add the four (Equation 4-22). TxDOT also uses the sum as a check on mixed-use coefficients, with judgment mainly in Cs.
The calculator is tested against the cases below every time its code changes.
| Case | What | Reference | Values compared | Largest difference | Result |
|---|---|---|---|---|---|
| The table loads with the calculator. The same results are in verification.json. | |||||
Weighted C and peak flows are compared with FHWA HEC-22 (4th ed.) Examples 4.1 and 4.3; intensities from NOAA Atlas 14 with NOAA PFDS values; the rest are hand calculations of Q = CiA.
- One outlet and one Tc. Partial-area effects (a smaller, faster part of the watershed giving a higher peak) are not checked.
- No hydrograph and no storage. For detention, use a hydrograph method.
- Runoff coefficients are a judgment: the C values tab lists the published FHWA ranges; your local criteria may set the values. The TxDOT HDM tables are reproduced as published; TxDOT itself calls Table 4-10 typical of design guides, and Table 4-11 is for rural watersheds.
- How do I choose C?
- From a table of land uses or surfaces, such as FHWA HEC-22 Table 4.1 or TxDOT HDM Tables 4-10 and 4-11 on the C values tab, or your local criteria manual. For mixed land use, enter the subareas separately; the calculator weights C by area.
- Why a 10-minute minimum?
- Very short durations give very high intensities that the method does not represent well for real watersheds. TxDOT and many cities use 10 minutes as the shortest duration for intensity; the Atlas 14 grid starts at 5 minutes.
- When is the Rational Method not appropriate?
- For large areas (FHWA and TxDOT: over about 200 acres), where storage such as ponds or detention is significant, or when a hydrograph is needed. Use an NRCS or unit hydrograph method instead.
- Can I attach the calculation sheet to a design report?
- You can print it and include it as a supporting calculation that you have checked. It is a calculation aid, not a sealed engineering document: the engineer of record reviews it and is responsible for the design, and the criteria of the reviewing agency decide which methods and values apply.
| Topic | Reference |
|---|---|
| Rational Method | FHWA (2024). Urban Drainage Design Manual, HEC-22, 4th ed., FHWA-HIF-24-006. |
| Texas practice | TxDOT Hydraulic Design Manual, Chapter 4, Section 12 — Rational Method. |
| Rainfall | Perica, S., et al. (2018). NOAA Atlas 14, Volume 11 Version 2.0: Texas. NOAA, National Weather Service. |
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A free calculation aid. This calculator applies the published methods named on this page to the inputs you enter. It is not a sealed engineering document, has not been reviewed by a licensed professional for your project, and no warranty is expressed or implied. Check the results independently before using them for design, bidding or permitting.
The criteria of the reviewing agency decide which methods and values apply to a design. The engineer of record is responsible for the design.
Using this calculator does not create an engineer–client relationship. Calculations run in your browser; your inputs are not sent to or stored by HERO E&C. HERO E&C · TBPELS Firm F-27793.