What is Horton's infiltration equation?

Horton's equation (1940) models how infiltration rate f(t) decreases exponentially from an initial rate f0 to a final steady-state rate fc: f(t) = fc + (f0 − fc) × e^(−kt), where k is the decay constant and t is time.

What are typical values for f0 and fc?

For sandy soil f0 ≈ 250 mm/hr, fc ≈ 25 mm/hr. For clay soil f0 ≈ 25 mm/hr, fc ≈ 1–3 mm/hr. Loam sits between these extremes. Values depend heavily on antecedent moisture.

What does the decay constant k represent?

k (units: 1/min or 1/hr) controls how fast the rate drops. A larger k means infiltration reaches steady state more quickly. Typical values range from 0.5 to 5 hr⁻¹ depending on soil texture.

How do I get f0, fc, and k from field data?

Run a double-ring infiltrometer test and record cumulative infiltration vs. time. Fit the Horton curve by regression or by reading f0 at t=0, fc at large t, and solving for k from an intermediate point.

Can I use minutes instead of hours?

Yes — just keep units consistent. If rates are in mm/min, k must be in 1/min and t in minutes. The tool accepts any consistent unit system; the label is flexible.

Infiltration Rate Calculator

Name: Infiltration Rate Calculator
Availability: InStock
Author: Nham Vu

Calculate soil water infiltration rate at any time using Horton's equation with initial rate, final rate, and decay constant.

Horton Equation Parameters

Initial infiltration rate f₀ (mm/hr or mm/min)

Rate at t = 0 (dry soil). E.g. 150 mm/hr for loam.

Final (steady-state) rate f_c (same unit)

Steady-state rate when soil is saturated. Must be ≤ f₀.

Decay constant k (1/hr or 1/min)

Controls how fast rate drops. Typical: 0.5–5 hr⁻¹.

Elapsed time t (same time unit as k)

Time at which to evaluate f(t).

Chart time range (max t) (same unit)

Result

Fill in the parameters and click Calculate.

Infiltration Rate vs. Time

Chart appears after first calculation.

Summary

Calculate soil water infiltration rate at any time using Horton's equation with initial rate, final rate, and decay constant.

How it works

Enter the initial infiltration rate (f0) — the rate at the start when soil is dry.
Enter the final (steady-state) infiltration rate (fc) — the rate once the soil is saturated.
Enter the decay constant (k) that controls how quickly the rate decreases.
Enter the elapsed time t in minutes.
The tool computes f(t) = fc + (f0 − fc) × e^(−kt) and displays the result.
Use the chart to visualize how infiltration rate changes over the full time range.

Use cases

Estimate when a field reaches steady-state infiltration during irrigation.
Design stormwater infiltration basins for a given soil type.
Calibrate Horton parameters against field double-ring infiltrometer data.
Compare infiltration curves for different soil textures (sand vs. clay).
Calculate cumulative infiltration over a specified time window.
Support hydrological runoff modeling and flood risk assessments.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu