Rainfall Runoff Rate Formulas and Calculator

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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, 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.

Regions of the United States for use with the Steel formula.

Figure 1 - Regions of the United States for use with the Steel formula.

Table 1.0 Coefficients for Steel Formula

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

References:

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