Inputs
Formula used
Curve Number runoff depth
Potential retention: S = 25400/CN - 254 (mm)
Initial abstraction: Ia = λS
Runoff depth (if P > Ia): Q = (P - Ia)^2 / (P + (1 - λ)S)
If P ≤ Ia, then Q = 0.
Rational peak discharge
In SI: Qp = 0.278 · C · i · A, where i is mm/hr and A is km², giving Qp in m³/s.
How to use this calculator
- Enter the catchment area and choose its unit.
- For runoff depth and volume, provide rainfall depth and a Curve Number.
- For peak flow, provide coefficient C and rainfall intensity.
- Optionally tick auto intensity to use depth ÷ duration.
- Add time of concentration to judge whether intensity duration fits.
- Press Submit to see results, then download CSV or PDF.
Example data table
| Scenario | Area | Rainfall depth | Duration | CN | λ | C | Intensity | Runoff depth | Runoff volume | Peak discharge |
|---|---|---|---|---|---|---|---|---|---|---|
| Sample watershed | 1.5 km² | 60 mm | 2 hr | 75 | 0.2 | 0.45 | 30 mm/hr | 14.5204 mm | 21780.58 m³ | 5.6295 m³/s |
Professional article
1) Rainfall-runoff purpose
Rainfall-runoff calculations translate storm input into runoff depth, volume, and peak flow for a catchment. This helps size culverts, drains, detention storage, and erosion controls. The calculator combines a depth-based method for event runoff with a peak-flow method commonly used for small basins and urban design checks.
2) Curve Number as a land response index
The Curve Number (CN) summarizes soil permeability, land cover, treatment, and antecedent moisture into one parameter. Higher CN values represent reduced infiltration and greater direct runoff. Because CN is bounded, it provides a consistent way to compare scenarios like pavement, compacted soil, grass, and woodland within a single event framework.
3) Storage potential and initial losses
The method computes a potential retention S from CN and then estimates initial abstraction Ia = λS. This captures early losses such as interception, surface wetting, and small depressions. A larger λ raises the rainfall threshold before runoff begins, reducing runoff for modest storms.
4) Runoff depth from storm depth
When rainfall depth P exceeds Ia, runoff depth Q increases nonlinearly through (P − Ia)^2. That curvature reflects how runoff accelerates once soils and surface storage are satisfied. When P ≤ Ia, the event produces zero direct runoff in this simplified representation.
5) Converting depth to runoff volume
Depth becomes volume by multiplying by catchment area. This is essential for detention sizing and water balance checks. The calculator reports volume in cubic meters and acre-feet to support both metric and customary workflows. Small changes in depth can create large volume differences when the drainage area is large.
6) Peak discharge using the Rational method
The Rational approach estimates peak discharge as Qp = 0.278·C·i·A in SI units, where C is a runoff coefficient, i is rainfall intensity, and A is area. It is most appropriate for short-duration storms and relatively small watersheds where intensity is reasonably uniform.
7) Intensity selection and time of concentration
Peak flow depends strongly on intensity duration. A practical rule is to use an intensity whose averaging duration is near the time of concentration. If the chosen storm duration is much shorter than Tc, the calculated peak may be inconsistent. The optional Tc input provides a quick reasonableness check.
8) Interpreting outputs and sensitivity
Compare methods rather than relying on one number. CN controls event runoff depth and volume, while C and i dominate peak discharge. Sensitivity testing—adjusting CN, λ, and intensity by realistic increments—reveals which assumptions drive results and supports defensible design documentation.
FAQs
1) What does CN represent?
CN is an index that summarizes infiltration and surface runoff behavior from soil type, land cover, treatment, and wetness. Higher CN generally means more direct runoff for the same rainfall event.
2) When should I change lambda?
Use the default 0.2 unless a study or guideline recommends another value. Increasing lambda delays runoff onset and reduces runoff for smaller storms by increasing the initial abstraction threshold.
3) Can I use depth divided by duration as intensity?
Yes for quick checks, but design intensity is usually taken from local intensity-duration-frequency data. Depth divided by duration can understate short, intense bursts that control peak flow.
4) What is a good runoff coefficient C?
C depends on surface type and drainage efficiency. Impervious, well-drained areas have higher C, while vegetated or permeable areas have lower C. Use values consistent with local standards for your setting.
5) Why do I need time of concentration?
Tc guides which rainfall duration best represents the peak-producing intensity. If intensity is based on a duration far from Tc, the estimated peak discharge may be biased high or low.
6) Why do CN and Rational results differ?
They answer different questions. CN estimates event runoff depth and volume, while the Rational method targets peak discharge. Differences are expected because they depend on different assumptions and inputs.
7) How should I document results?
Record inputs, selected parameters, and the chosen intensity basis. Export the CSV or PDF report, then note the design scenario, return period source for intensity, and any sensitivity runs used to justify assumptions.