Infiltration Calculator

With f₀ = 60 mm/h, fc = 10 mm/h and k = 2 h⁻¹, 31.6166 mm infiltrates in the first hour.

Model:

Horton: f = fc + (f₀ − fc) e^(−kt)Kostiakov: F = a tᵇ

Initial infiltration rate f₀ (mm/h):

Final (basic) infiltration rate fc (mm/h):

Decay constant k (1/h):

Time t (h):

Cumulative infiltration F =

31.6166179190847 mm

Precision

Full answer, then cut to fewer decimals (not rounded):

31.6166179190847 mm
31.616617919084 mm
31.61661791908 mm
31.6166179190 mm
31.616617919 mm
31.61661791 mm
31.6166179 mm
31.616617 mm
31.61661 mm
31.6166 mm
31.616 mm
31.61 mm
31.6 mm

Infiltration rate at t: 16.76676416 mm/h
Average rate over t: 31.61661792 mm/h

Step-by-step solution

f = fc + (f₀ − fc)e^(−kt) = 16.76676416 mm/h
F = fc t + (f₀ − fc)(1 − e^(−kt))/k = 31.61661792 mm

Infiltration Formula

f = fc + (f₀ − fc) e^(−kt)

F = fc t + (f₀ − fc)(1 − e^(−kt))/k; Kostiakov F = a tᵇ

Worked Example

Horton with f₀ = 60 mm/h, fc = 10 mm/h and k = 2 per hour after one hour:

f = fc + (f₀ − fc)e^(−kt) = 16.76676416 mm/h
F = fc t + (f₀ − fc)(1 − e^(−kt))/k = 31.61661792 mm

Average rate over t: 31.61661792 mm/h

GATE tip

Horton’s F is the integral of f: remember the (1 − e^(−kt))/k term when a question asks for depth, not rate.

More Soil and Water Conservation Engineering Calculators

USLE Soil Loss Calculator

A = R K LS C P

LS = (λ/22.13)^m (65.41 sin²θ + 4.56 sin θ + 0.065)

Example: R = 800, K = 0.03, LS = 1.2, C = 0.3 and P = 0.5: Average annual soil loss A = 4.32 t/(ha·yr).

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SCS Curve Number Calculator

Q = (P − Ia)² / (P − Ia + S)

S = 25,400/CN − 254 mm; Ia = λS (λ = 0.2)

Example: 100 mm of rain on a catchment with CN = 75: Direct runoff Q = 41.1371 mm.

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Frequently asked questions

What is the basic infiltration rate?

The nearly constant rate fc reached after long wetting; it governs sprinkler and surface irrigation design.

How is Kostiakov fitted?

Plot log F against log t from a double-ring test: the slope is b and the intercept log a.

Sources

The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

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APA

Scientific Converters. (2026, October 15). Infiltration Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/infiltration-calculator/

IEEE

Scientific Converters, "Infiltration Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/infiltration-calculator/