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### Rainfall Runoff Rate Formulas and Calculator

Civil Engineering and Design

Rainfall Runoff Rate On Minor Size Land Formulas and Calculator

The most common means for determining runoff for minor hydraulic structures is the rational formula:

Eq. 1
Q = C · I · A

Where:

Q = peak discharge, ft3/s (m3/s)
C = runoff coefficient = percentage of rain that appears as direct runoff
I = rainfall intensity, in/h (mm/h)
A = drainage area, acres (m2)

Drainage area = land area (in2) x depth + runoff volume onto land (in3)

Rainfall Intensity Formula

Chow lists 24 rainfall-intensity formulas of the form:

Eq. 2
I = K · Fn1 / ( t + b )n

Where:

I = rainfall intensity, in/h (mm/h)
K, b, n, and n1 = coefficient, factor, and exponents, respectively, depending on conditions that affect rainfall intensity, see Table 1.0
F = frequency of occurrence of rainfall, years
t = duration of storm, min,
= time of concentration

Reference
1 gal/sec = 60.0 gal/min = 3600 gal/hr
cu-ft = ft3
Sq.-m = m3

The most useful of these rainfall-intensity formulas is the Steel formula:

Eq. 3
I = K / ( t + b )

The Steel formula gives the average maximum precipitation rates for durations up to 2 h. Figure 1 - Regions of the United States for use with the Steel formula.

Table 1.0 Coefficients for Steel Formula

 Frequency Years Coefficients Region 1 2 3 4 5 6 7 2 K 206 140 106 70 70 68 32 b 30 21 17 13 16 14 11 4 K 247 190 131 97 81 75 48 b 29 25 19 16 13 12 12 10 K 300 230 170 111 111 122 60 b 36 29 23 16 17 23 13 25 K 327 260 230 170 130 155 67 b 33 32 30 27 17 26 10

Where:

• K and b are dependent on the storm frequency and region of the United States (Fig. 1.0 and Table 1.0).
• The Steel formula gives the average maximum precipitation rates for durations up to 2 h.

Related:

References:

• Civil Engineering Formulas 2009, Tyler G. Hicks, P.E.,