Rational method calculator
Peak runoff Q = Cf·C·i·A from the runoff coefficient, rainfall intensity and drainage area, with the frequency factor for the storm.
PRELIMINARYReference tables are still being checked against their printed sources. How results are checked
- Frequency factor Cf
- 1.00
- Cf · C
- 0.32
The link carries these inputs, not the answer.
Worked example
The default inputs above are a published example: HEC-22 4th ed. Example 4.3, proposed condition, 10 yr: published Q = 31.4 cfs.
- Cf for the 10-yr storm = 1.00
- Q = 1.00 × 0.315 × 2.30 in/hr × 43.30 ac = 31.37 cfs
The formula
Q = Cf · C · i · A
FHWA HEC-22 4th ed. (2024) eq. 4.1, p. 23; Cf from HEC-22 3rd ed. (2009) p. 3-7
- Q
- peak runoff rate, cfs
- Cf
- frequency factor for the storm (HEC-22 3rd ed.)
- C
- runoff coefficient, area-weighted for mixed cover
- i
- rainfall intensity for a duration equal to Tc, in/hr
- A
- drainage area, ac
The frequency factor
HEC-22 3rd edition gives Cf as a correction some agencies apply to C for rarer storms, and says it is not endorsed by FHWA. The 4th edition (2024) keeps the paragraph and drops the table, so the 3rd edition table is the one to cite. No source read for this page states a cap on Cf · C, so the calculator warns above 1.0 and does not clamp.
| Return period | Cf |
|---|---|
| Tr < 25 years | 1.00 |
| Tr = 25 years | 1.10 |
| Tr = 50 years | 1.20 |
| Tr = 100 years | 1.25 |
The rational method and NYSDEC
The New York design manual names TR-55 and TR-20, or an approved equivalent, for the peak rates behind the channel protection, overbank and extreme flood criteria (DM2024 §§ 4.6 to 4.8). Use the rational method where the town, the county or a utility asks for it, and the NRCS method for the NYSDEC checks.
Questions about this calculation
- What is the rational formula?
- Q = C i A, with Q in cfs, i in in/hr and A in acres. With a frequency factor it is Q = Cf C i A.
- FHWA HEC-22 4th ed. (2024) eq. 4.1, p. 23
- What duration is the rainfall intensity for?
- A duration equal to the time of concentration of the drainage area.
- HEC-22 4th ed. p. 24
- How large an area can the rational method handle?
- HDS-2 recommends it for drainage areas under 200 ac.
- HEC-22 4th ed. p. 25
- What are the Cf values?
- 1.0 below 25 yr, 1.1 at 25 yr, 1.2 at 50 yr and 1.25 at 100 yr. FHWA does not endorse the factor.
- HEC-22 3rd ed. § 3.2.2.1, p. 3-7
- How do I weight C for mixed cover?
- By area: C = Σ(C × A) / ΣA.
- HEC-22 4th ed. eq. 4.2, p. 25
- Can I use the rational method for NYSDEC Qp and Qf?
- The design manual names TR-55 and TR-20, or an approved equivalent, for those peak rates.
- NYSDEC DM2024 §§ 4.6 to 4.8
The other calculators
- Curve number and runoff. Composite CN from cover type and hydrologic soil group, then TR-55 runoff depth for a 24-hr rainfall.
- Time of concentration. TR-55 Tc from a sheet flow, a shallow concentrated flow and a channel flow segment, in hours and minutes.
- Detention volume estimate. Storage needed to hold post-development runoff to an allowable release rate, by the modified rational critical-duration method.
- NY water quality volume. WQv = P·Rv·A/12 from the 90th percentile rainfall, impervious cover and contributing area, per the NYSDEC design manual.
The full app runs the whole site: Atlas 14 rainfall frozen for the project, pre and post hydrographs, and the pond routed through its outlets. Then the NYSDEC checks you select, and a PDF report with the SWMM file a reviewer can rerun.
14-day trial, every feature, no card.