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Calcimator

Rational Method Runoff

Calculate peak stormwater discharge using the Rational Method (Q = CIA/360). Estimate runoff from rainfall intensity, runoff coefficient, and catchment area.

About this calculator

The Rational Method is the oldest and simplest peak-discharge formula in stormwater engineering: Q = CIA, where C is a dimensionless runoff coefficient, I is rainfall intensity, and A is catchment area. In the metric units used here (Q in cubic meters per second, I in millimeters per hour, A in hectares), the /360 divisor is not a rounded rule of thumb -- it is the exact unit-conversion factor (1 hectare = 10,000 m^2, and mm/hr to m/s introduces a factor of 1000 x 3600), so this calculator's Peak Discharge is dimensionally exact given the C, I, and A you enter, with no approximation in the arithmetic itself. The approximation is entirely in the inputs: C is a lumped estimate of how much of a storm becomes runoff rather than infiltrating or being stored, and it varies with soil type, slope, antecedent moisture, and land cover, not just the land-use label.

Runoff Volume (1hr Storm) is Peak Discharge sustained for exactly one hour -- a simplification, not the integral of a real storm hydrograph, which rises and falls rather than holding a constant rate. Effective Impervious % is simply the Runoff Coefficient read as a percentage, a common rough proxy in introductory hydrology texts, not a literal measured impervious-cover survey. The Rational Method itself is only appropriate for small, fairly uniform catchments where the storm duration roughly matches the time of concentration; it produces one peak-flow number, not a full hydrograph, and most drainage design guidance caps its use at catchment areas on the order of a few hundred hectares or less -- beyond that, or for watersheds with mixed land cover and long flow paths, NRCS curve-number or full hydrograph methods are the standard replacement.

Inputs

mm/hr
ha

Results

Peak Discharge

0.694 m³/s

Peak Discharge

694.44 L/s

Peak Discharge (Imperial)24.52 cfs
Flow Rate11,007.15 GPM
Runoff Volume (1hr Storm)2,500 m³
Effective Impervious %50%
How to Use This Calculator
  1. Enter Rainfall Intensity, Runoff Coefficient (C), and Catchment Area.
  2. Review Peak Discharge (m³/s) and Peak Discharge (L/s).
  3. Use Peak Discharge (Imperial) (cfs) and Flow Rate (GPM) to inform your decision.
  4. Use the chart to visualize the results and explore different scenarios by adjusting inputs.

How the result changes with Rainfall Intensity

Rainfall IntensityPeak DischargePeak Discharge
250.347 m³/s347.22 L/s
380.528 m³/s527.78 L/s
751.042 m³/s1,041.67 L/s
1251.736 m³/s1,736.11 L/s

What each input means

Rainfall Intensity
Design rainfall intensity for the chosen return period and time of concentration
Runoff Coefficient (C)
Fraction of rainfall becoming runoff; 0.1 = forest, 0.5 = suburban, 0.9 = pavement
Catchment Area
Drainage area contributing to the design point in hectares (1 ha = 10,000 m²)

How this is calculated

Formula

Q = C × I × A / 360

Worked example, using the default values

  1. Identify Input Parameters
    Rainfall Intensity = 50, Runoff Coefficient (C) = 0.5, Catchment Area = 10 = 3 input(s) provided
  2. Calculate Peak Discharge
    Peak Discharge
    0.694 = 0.694
  3. Calculate Peak Discharge
    Peak Discharge
    694.44 = 694.44
  4. Calculate Peak Discharge
    Peak Discharge
    24.52 = 24.52
  5. Calculate Flow Rate
    Flow Rate
    11007.15 = 11007.15

Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Is the /360 divisor an approximation, like the imperial Rational Method's Q = CiA?

No -- in this calculator's metric units (Q in m^3/s, rainfall intensity in mm/hr, area in hectares), 360 is the exact algebraic conversion factor, not a rounded constant. The commonly cited imperial version, Q = CiA with Q in cfs, i in in/hr, and A in acres, actually carries a small rounding (1 acre-inch/hour is about 1.008 cfs, conventionally dropped to 1); the metric form used here has no equivalent rounding to drop.

What does Runoff Volume (1hr Storm) actually represent?

It is Peak Discharge multiplied by 3,600 seconds -- the volume you would get if the peak flow rate held perfectly constant for one full hour. Real storms don't produce a rectangular hydrograph; discharge rises to a peak and falls off on both sides, so the true volume of runoff from an actual storm is generally less than this figure. Treat it as an upper-bound planning number, not a metered volume.

Can I cite the 0.1 forest / 0.5 suburban / 0.9 pavement examples for a permit application?

Treat them as illustrative starting points from general civil engineering references, not an approved regulatory table. Runoff coefficients that matter for a real drainage permit come from your local jurisdiction's drainage design manual, which sets C by soil group, slope, and land-use category specific to that city, county, or state DOT -- those values can differ meaningfully from generic textbook examples, so confirm against the local manual before submitting anything.

When is the Rational Method the wrong tool, even with accurate inputs?

Once the catchment gets large, has mixed land cover, or has flow paths long enough that the storm duration can no longer be assumed to match the time of concentration across the whole area, the Rational Method's core assumption breaks down. Most agencies cap its use at catchments on the order of a few hundred hectares; beyond that, or when you need a full runoff hydrograph rather than one peak number, NRCS curve-number or hydrograph-based methods are the standard replacement.

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