Estimate peak stormwater runoff using Q = CiA for a small catchment. Combine runoff coefficients across subareas and follow the unit conversions.
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Worked examples
These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.
Example 1
US single catchment: C=0.3, i=2 in/hr, A=5 ac
Given
subareas
1.runoff coefficient 0.3area 5 ac
intensity
2 in/hr
Assumptions
Rational method assumptions: storm duration ≥ time of concentration, uniform rainfall over the catchment, and runoff coefficient constant during the storm.
Solution steps
Rational formula
Peak flow is runoff coefficient × rainfall intensity × drainage area, in consistent units.
Qp = C · i · A
Qp = 0.3 × 2 in/h × 5 ac = 3.025 cfs
= 3.025 cfs
Handbook form check
The familiar US form Q(cfs) ≈ C · i(in/hr) · A(ac) treats 1 ac·in/hr as exactly 1 cfs; it is actually 1.008 cfs, which is why the exact answer differs slightly from the shortcut.
Shortcut: Q ≈ 3 cfs vs exact 3.025 cfs
Results
Peak runoff Qp
3.025cfs
Composite runoff coefficient Cw
0.3
Total drainage area
5ac
Where this answer was checked
source
Rational formula (NCEES FE Reference Handbook); exact unit conversion — Q = C·i·A with ac·in/hr → cfs carrying the 1.00833 factor
Rational method assumptions: storm duration ≥ time of concentration, uniform rainfall over the catchment, and runoff coefficient constant during the storm.
Solution steps
Rational formula
Peak flow is runoff coefficient × rainfall intensity × drainage area, in consistent units.
Qp = C · i · A
Qp = 0.6 × 80 mm/h × 2 ha = 0.2667 m^3/s
= 0.2667 m^3/s
Results
Peak runoff Qp
0.2667m^3/s
Composite runoff coefficient Cw
0.6
Total drainage area
2ha
Where this answer was checked
source
Rational formula (NCEES FE Reference Handbook) — Q = C·i·A in coherent SI
verified by
hand-recomputed
derivation
i = 0.08/3600 = 2.2222e-5 m/s; A = 20000 m²; Q = 0.6·2.2222e-5·20000 = 0.26667 m³/s.
Example 3
composite catchment: 2 ac at C=0.9 + 8 ac at C=0.3, i=3 in/hr
Given
subareas
1.runoff coefficient 0.9area 2 ac
2.runoff coefficient 0.3area 8 ac
intensity
3 in/hr
Assumptions
Rational method assumptions: storm duration ≥ time of concentration, uniform rainfall over the catchment, and runoff coefficient constant during the storm.
Solution steps
Composite runoff coefficient
Weight each subarea's C by its area.
Cw = Σ(Ci·Ai) / Σ(Ai)
Cw = (0.9 × 2 ac + 0.3 × 8 ac) / 10 ac = 0.42
= 0.42
Rational formula
Peak flow is runoff coefficient × rainfall intensity × drainage area, in consistent units.
Qp = C · i · A
Qp = 0.42 × 3 in/h × 10 ac = 12.71 cfs
= 12.71 cfs
Handbook form check
The familiar US form Q(cfs) ≈ C · i(in/hr) · A(ac) treats 1 ac·in/hr as exactly 1 cfs; it is actually 1.008 cfs, which is why the exact answer differs slightly from the shortcut.
Shortcut: Q ≈ 12.6 cfs vs exact 12.71 cfs
Results
Peak runoff Qp
12.71cfs
Composite runoff coefficient Cw
0.42
Total drainage area
10ac
Where this answer was checked
source
Rational formula with area-weighted composite C — Cw = ΣCᵢAᵢ/ΣAᵢ, then Q = Cw·i·A