Learn: Rational Method runoff
The Rational Method estimates a peak runoff rate for a catchment using rainfall intensity, catchment area and a runoff coefficient. It is a peak-flow estimate, not the full time history of a storm.
What the formula is saying
Rainfall intensity i multiplied by area A gives the incoming rainfall volume per second. Multiplying by runoff coefficient C estimates the portion contributing to the modeled peak runoff.
Read the symbols in plain language
- C
- Runoff coefficient
Runoff coefficient. The coefficient scales incoming rainfall to the modeled peak runoff contribution.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- i
- Rainfall intensity
Rainfall intensity. A depth rate multiplied by catchment area gives the rainfall volume arriving each second.
m/sUse m/s as the base unit shown here. This calculator uses consistent SI units: i in m/s, A in m² and Q in m³/s. Convert mm/h to m/s by dividing by 3600000. C is a decimal fraction between 0 and 1, not a whole-number percentage.
- A
- Catchment area
Catchment area. A depth rate multiplied by catchment area gives the rainfall volume arriving each second.
m²Square metres measure area; square the length conversion factor.
- Q
- Result to find
Rational Method runoff. The coefficient scales incoming rainfall to the modeled peak runoff contribution.
m³/s
Sort out the units first
This calculator uses consistent SI units: i in m/s, A in m² and Q in m³/s. Convert mm/h to m/s by dividing by 3600000. C is a decimal fraction between 0 and 1, not a whole-number percentage.
Assumptions before calculating
Assume rainfall intensity appropriate to the chosen frequency and a duration at least matching the catchment time of concentration, approximately uniform rainfall, and a coefficient suitable for the catchment and event.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find Q and explain the result in the stated output unit.
- C · Runoff coefficient
- 0.7
- i · Rainfall intensity
- 0.00002778 m/s
- A · Catchment area
- 10000 m²
Convert rainfall intensity into a volume rate
A depth rate multiplied by catchment area gives the rainfall volume arriving each second.
(0.00002778) × (10000) = 0.2778 m³/sApply the runoff coefficient
The coefficient scales incoming rainfall to the modeled peak runoff contribution.
(0.7) × (0.2778) = 0.19446 m³/s
Does this worked answer make sense?
The estimated peak cannot exceed iA for 0 ≤ C ≤ 1 in this model. Doubling area doubles Q only when the same intensity and runoff coefficient remain applicable.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- C · Runoff coefficient
- 0.5
- i · Rainfall intensity
- 0.00002 m/s
- A · Catchment area
- 20000 m²
Convert rainfall intensity into a volume rate
A depth rate multiplied by catchment area gives the rainfall volume arriving each second.
(0.00002) × (20000) = 0.4 m³/sApply the runoff coefficient
The coefficient scales incoming rainfall to the modeled peak runoff contribution.
(0.5) × (0.4) = 0.2 m³/s
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- C · Runoff coefficient
- 0.8
- i · Rainfall intensity
- 0.000025 m/s
- A · Catchment area
- 15000 m²
Find: Learn: Rational Method runoff
A hint, not the answer
Rainfall intensity i multiplied by area A gives the incoming rainfall volume per second. Multiplying by runoff coefficient C estimates the portion contributing to the modeled peak runoff.
This calculator uses consistent SI units: i in m/s, A in m² and Q in m³/s. Convert mm/h to m/s by dividing by 3600000. C is a decimal fraction between 0 and 1, not a whole-number percentage.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Convert rainfall intensity into a volume rate
A depth rate multiplied by catchment area gives the rainfall volume arriving each second.
(0.000025) × (15000) = 0.375 m³/sApply the runoff coefficient
The coefficient scales incoming rainfall to the modeled peak runoff contribution.
(0.8) × (0.375) = 0.3 m³/s
Avoid the common trap
Do not combine intensity in mm/h and area in hectares with this SI equation without conversion. Do not describe the result as storm runoff volume, and do not treat a supplied C as a universal constant.
When this method applies — and when it does not
Applicability depends on catchment size, storage and local drainage guidance. This simplified method does not route a hydrograph, model changing infiltration or establish a design storm. Do not apply a coefficient copied from an unrelated surface or jurisdiction.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Rational Method runoff. Hydrologic and drainage-system principles, including Rational Method assumptions, rainfall intensity, catchment response and hydraulic losses.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.