In short: peak runoff from a watershed or site is Q = C × i × A — the runoff coefficient times the rainfall intensity times the drainage area. A 10-acre medium-density residential area (C = 0.40) in a 2 in/hr design storm produces about 8.0 cfs (3,590.6 GPM) of peak runoff. Paved or roofed surfaces produce far more runoff than lawns or woods for the same storm.
This is a planning-level estimate. Stormwater infrastructure design should follow your local drainage manual and be reviewed by a licensed engineer.
How to calculate watershed runoff (the Rational Method)
The Rational Method estimates the peak rate of stormwater runoff from a drainage area during a design storm. It multiplies three things: how much of the rain actually runs off instead of soaking in (the runoff coefficient), how hard it's raining (intensity), and how big the area is:
This calculator converts whatever area and intensity units you enter into acres and inches per hour, multiplies by the coefficient, and reports the peak flow in cfs, GPM, MGD, m³/s and L/s. It does not estimate the total volume of a storm or how the flow changes over time — only the single peak rate a downstream pipe, channel or inlet needs to carry.
Worked example. Take a 10-acre medium-density residential area (C = 0.40) in a storm producing 2.0 in/hr. Multiply: 0.40 × 2.0 × 10 = 8.0 cfs. Converting, that's about 3,590.6 GPM or 226.5 L/s — see the storm drain size calculator for the next step, sizing a pipe to carry that flow.
Runoff vs. streamflow. This calculator estimates runoff generated by a storm over a drainage area — it is not the same as measuring flow in an existing stream or channel. For that, see the streamflow calculator, which uses channel cross-section and velocity instead.
Why the runoff coefficient changes the answer
The runoff coefficient (C) represents the fraction of rainfall that becomes surface runoff rather than infiltrating into soil, evaporating, or being intercepted by vegetation. Impervious surfaces like pavement and roofs let almost none of the rain soak in, so C sits near 0.90–0.95. Lawns, parks and forested land absorb much more, so C drops to 0.10–0.20. A watershed's overall coefficient is the area-weighted average of every surface type within it — a parking lot next to a park behaves very differently from either surface alone.
Rainfall intensity has an equally direct effect: a storm with twice the intensity produces twice the peak flow for the same area and coefficient. Because intensity depends on both storm severity and how quickly the drainage area concentrates flow (time of concentration — a shorter time of concentration usually means a higher design intensity), it is normally read from a local Intensity-Duration-Frequency (IDF) curve rather than assumed.
Typical runoff coefficients by land cover
Representative Rational Method values used in US drainage practice. Actual values vary with slope, soil type and local design standards — always confirm against your jurisdiction's drainage manual for design work.
| Land cover | Typical C |
|---|---|
| Pavement (asphalt / concrete) | 0.95 |
| Roofs | 0.90 |
| Commercial / downtown | 0.85 |
| Industrial | 0.70 |
| Residential — multi-family (attached) | 0.65 |
| Residential — single-family (medium lot) (default) | 0.40 |
| Residential — single-family (large lot, >½ acre) | 0.30 |
| Cultivated / agricultural land | 0.30 |
| Parks & lawns (clay soil) | 0.20 |
| Woods / forest | 0.15 |
| Parks & lawns (sandy soil) | 0.10 |
Worked examples
Residential subdivision
8.0 cfs
10 acres of medium-density residential (C = 0.40) in a 2.0 in/hr design storm produces about 8.0 cfs, or 3,590.6 GPM.
Shopping center parking lot
13.5 cfs
5 acres of pavement (C = 0.90) in a 3.0 in/hr storm produces about 13.5 cfs, or roughly 6,059.2 GPM — nearly twice the flow of the subdivision above from half the area.
Wooded natural area
6.0 cfs
40 acres of woods (C = 0.10) in a 1.5 in/hr storm produces about 6.0 cfs — a fraction of what the same rainfall would produce over paved ground.
What else affects the result
Time of concentration. The Rational Method assumes the storm lasts at least as long as it takes water from the farthest point in the watershed to reach the outlet. Using an intensity for a shorter storm than this understates the true peak; your IDF curve lookup should already account for it.
Antecedent soil moisture. Ground that is already saturated from previous rain sheds water faster than dry soil, effectively raising C for that event. Design coefficients are typically chosen to be reasonable across a range of moisture conditions rather than for a single storm.
Watershed size. The Rational Method is generally considered reliable for drainage areas up to about 200 acres. Larger or more complex watersheds are usually modeled with a method such as NRCS TR-55 or a full hydrologic/hydraulic model, which account for storage and routing effects this formula ignores.
Slope and shape. Steeper or more elongated watersheds concentrate flow faster, which shortens time of concentration and can raise the design rainfall intensity even without changing land cover. For sizing what happens downstream of this calculation, see the catch basin sizing calculator.
Frequently asked questions
What is the Rational Method formula for runoff?
The Rational Method is Q = C × i × A, where Q is peak runoff in cubic feet per second, C is a dimensionless runoff coefficient between 0 and 1, i is rainfall intensity in inches per hour, and A is the drainage area in acres. It is the most widely used formula for sizing small stormwater systems in the United States.
What runoff coefficient (C) should I use?
The runoff coefficient depends on land cover. Pavement and roofs are around 0.90–0.95, dense residential areas are around 0.60–0.65, lawns and parks are around 0.10–0.20, and woods or undisturbed natural land are around 0.10–0.15. Use a weighted average when a site has more than one land cover.
Where does the rainfall intensity value come from?
Rainfall intensity for a design storm comes from a local Intensity-Duration-Frequency (IDF) curve, matched to the time of concentration of the drainage area and the design storm return period your jurisdiction requires. It is not a typical or average rainfall rate.
How accurate is the Rational Method?
The Rational Method is a well-established planning-level estimate, generally considered reliable for drainage areas up to about 200 acres. For larger or more complex watersheds, hydrologists typically use methods such as NRCS TR-55 or a full hydrologic model instead.
Does this calculator account for time of concentration?
No. This calculator computes peak flow from a runoff coefficient, a rainfall intensity you supply, and an area. Time of concentration is used upstream of this calculation, to pick the correct rainfall intensity from an IDF curve, and is not itself an input to the Q=CiA formula.
Is this calculator suitable for stormwater system design?
It is a planning aid for quick estimates. Actual stormwater infrastructure design should follow your local drainage design manual and be reviewed by a licensed engineer, since jurisdictions often specify required return periods, coefficients and methods.
Sources & references
- Kuichling, E. (1889). The relation between the rainfall and the discharge of sewers in populous districts. Transactions of the ASCE, 20, 1–56.
- American Society of Civil Engineers (ASCE) & Water Environment Federation. Design and Construction of Urban Stormwater Management Systems, Manual of Practice No. 77.
- USDA Natural Resources Conservation Service (NRCS). National Engineering Handbook, Part 630 — Hydrology.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)