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Rainfall Runoff Rate Formulas and Calculator
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, ft^{3}/s (m^{3}/s)
C = runoff coefficient = percentage of rain that appears as direct runoff
I = rainfall intensity, in/h (mm/h)
A = drainage area, acres (m^{2})
Drainage area = land area (in^{2}) x depth + runoff volume onto land (in^{3})
Rainfall Intensity Formula
Chow lists 24 rainfallintensity formulas of the form:
Eq. 2
I = K · F^{n1} / ( 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
cuft = ft^{3}
Sq.m = m^{3}
The most useful of these rainfallintensity 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.
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References:
 Civil Engineering Formulas 2009, Tyler G. Hicks, P.E.,