Calculator
Storm water runoff calculator using the rational method.
Enter the catchment area, the surfaces it is made of and the rainfall intensity to get the peak storm water runoff in m³/s, litres per second and m³/h, worked out in your browser.
What this calculator does
The rational method estimates the peak storm water runoff from a small catchment: how many cubic metres per second a drain, culvert or outfall has to carry at the height of a storm. Enter the catchment area, the runoff coefficient (or the mix of surfaces it is made of) and the rainfall intensity, and the calculator gives the peak flow in m³/s, litres per second and m³/h. It is the same quick check a city engineer does before asking whether a drain is big enough, and it pairs naturally with ward-level flood alerts in CityWatch, which watch rain rate and channel trend live instead of on paper.
How it is calculated
In metric units the rational formula is:
Q = C × i × A ÷ 360
- Q is the peak runoff in cubic metres per second (m³/s).
- C is the runoff coefficient, the share of rain that runs off rather than soaking in or ponding (0 to 1).
- i is the rainfall intensity in millimetres per hour for a storm lasting as long as the catchment’s time of concentration.
- A is the catchment area in hectares.
- The 360 converts units: 1 mm/h falling on 1 hectare is 10 m³ per hour, or 1/360 m³ per second.
When a catchment has several kinds of surface, the calculator uses an area-weighted coefficient: weighted C = (C₁ × share₁ + C₂ × share₂ + C₃ × share₃) ÷ (share₁ + share₂ + share₃). Litres per second are Q × 1,000 and cubic metres per hour are Q × 3,600.
Worked example (illustrative)
Take an illustrative 5-hectare residential block: 30% roofs at C = 0.90, 30% roads and paving at C = 0.85 and 40% gardens and parks at C = 0.20, with a design rainfall intensity of 50 mm/h. These are the calculator’s default values, not figures for any real place.
- Weighted C = (0.90 × 30 + 0.85 × 30 + 0.20 × 40) ÷ 100 = (27 + 25.5 + 8) ÷ 100 = 0.605.
- Q = 0.605 × 50 × 5 ÷ 360 = 151.25 ÷ 360 ≈ 0.420 m³/s.
- That is about 420 litres per second, or 1,512.5 m³ per hour, at the peak.
Pave the gardens over (C = 0.85) and the weighted C rises to 0.865, which takes the peak to about 0.60 m³/s from the same storm on the same drains. That is why infill development floods streets that never flooded before.
Choosing the inputs
- Runoff coefficient. The picker fills in typical starting values (roofs 0.90, paved roads 0.85, parks 0.20 and so on). They are illustrative; take the coefficient for your surface, slope and soil from the tables in the official manual and overwrite the value.
- Rainfall intensity. Read it from the intensity-duration-frequency (IDF) curve for your city, at a duration equal to the time of concentration and for the return period your design standard sets. Do not use a daily rainfall total divided by 24; short bursts are far more intense than the daily average.
- Time of concentration. The time water takes to travel from the farthest point of the catchment to the point you are checking: inlet time plus time of flow in the drain. Use the method your design standard prescribes.
- Area. Measure the area that actually drains to the point you are checking, from a drainage map rather than a ward boundary.
Limits: a planning estimate, not a drain design
The rational method assumes uniform rain over the whole catchment for at least the time of concentration, and it gives a peak flow, not a hydrograph. That holds for small urban catchments: a housing block, a market, a stretch of road, a single outfall. For large or mixed catchments, or where storage, ponds and pumping change the timing, drainage manuals move to hydrograph methods and hydraulic models. Use this result to sense-check a drain or brief a meeting; size a drain with a qualified engineer and the design rules in the CPHEEO Manual on Storm Water Drainage Systems, Volume I Part A: Engineering Design (MoHUA). Coefficients, intensities and any catchment-size limits here are illustrative; confirm with your adviser / the official source.
Where CityWatch fits
A runoff estimate tells you what a drain should carry; it cannot tell you what is happening tonight. CityWatch puts rain gauges, channel levels, pump telemetry and citizen complaints on one live map, proposes an alert with the wards at risk when rain rate and channel trend cross a threshold, and shows pumps as running, offline or “no telemetry”. Read how flood early warning works in a city, and use the monsoon preparedness checklist for municipalities to get drains and crews ready before the season.
Questions
What is the rational method formula for runoff?
In metric units Q = C × i × A ÷ 360, where Q is peak runoff in m³/s, C the runoff coefficient, i the rainfall intensity in mm/h and A the catchment area in hectares.
How do I calculate a weighted runoff coefficient?
Multiply each surface’s coefficient by its share of the area, add the results and divide by the total share. For 30% roofs at 0.90, 30% roads at 0.85 and 40% lawns at 0.20, weighted C is 0.605.
Which rainfall intensity should I use in the rational method?
The intensity from your city’s intensity-duration-frequency curve for a storm lasting as long as the time of concentration, at the return period your design standard specifies.
When should the rational method not be used?
For large catchments, or where ponds, storage or pumping change the timing of flow. Drainage manuals use hydrograph methods and hydraulic models there.
See it on your own data. CityWatch — Warn before the street floods. Book a 30-minute working session with an engineer.