Horton Infiltration Rate Calculator

How Horton infiltration estimates describe soil intake during wetting

Horton infiltration capacity does not usually remain constant from the first minute of rainfall or irrigation to the last. A dry soil surface can take in water rapidly at the start of wetting, then slow as the upper soil becomes wetter, pore spaces fill, and surface sealing or compaction begins to matter. Horton’s equation represents that pattern with a declining curve: the rate begins near an initial capacity and gradually approaches a lower long-run capacity. This calculator converts that curve into two useful estimates: infiltration capacity at a chosen time and cumulative depth that could infiltrate over the same interval.

For stormwater, irrigation, erosion control, and preliminary runoff screening, the distinction between those two Horton results matters. When rainfall intensity stays below infiltration capacity, water can keep entering the ground without ponding. When rainfall intensity exceeds that capacity, the excess water becomes available for surface storage or runoff. One rate cannot capture the full change because soil behavior near the start of wetting can differ greatly from behavior later in an event. Horton’s model provides a compact estimate of both the changing rate and the accumulated depth.

This Horton calculator is intended to support more than a single button press. The sections below identify each parameter, explain the required units, show the rate and cumulative-depth equations, and describe how to read the outputs. Whether you are comparing site conditions, testing irrigation durations, or checking whether a storm may outpace soil intake, use this as a first-pass estimate before field calibration or a more detailed hydrologic analysis.

What Horton infiltration inputs mean in practice

The Horton infiltration calculation uses four inputs: initial infiltration capacity f₀, final infiltration capacity f_c, decay constant k, and elapsed time t. Together, these values describe the starting soil intake rate, the lower rate approached during continuing wetting, the speed of decline, and the duration of the infiltration opportunity.

Initial infiltration capacity, f₀: this is the high starting rate, usually associated with relatively dry conditions at the beginning of rainfall or irrigation. A loose, dry, or well-structured surface may have a fairly large initial value. In the standard Horton form, this number should be at least as large as the final capacity, because the curve declines over time rather than rising.

Final infiltration capacity, f_c: this is the lower rate the soil approaches after it has been wet for a while. It does not mean the soil instantly reaches a perfectly constant value, but it represents the long-run capacity in the model. In many real settings, this is the number that matters most for later storm periods, because runoff risk increases when the soil has already lost its early intake advantage.

Decay constant, k: this term controls how fast the Horton curve falls from f₀ toward f_c. Larger values of k mean a quicker decline. Smaller values keep the infiltration capacity elevated for longer. The units must match the time basis you use. In this calculator, k is entered in reciprocal hours, so the time input should also be in hours.

Elapsed time, t: this is the number of hours since the infiltration opportunity began. It can represent the duration since rainfall started, the duration of irrigation, or the duration of a field infiltration test. The calculator evaluates the Horton curve at that selected moment, then computes cumulative infiltrated depth from time zero to that same point.

Horton infiltration input errors often come from mismatched units rather than from the equation itself. If field notes are in minutes while k remains in 1/hr, the output will be wrong even though the calculation is correct. Keep the capacity terms in mm/hr, keep k in 1/hr, and enter time in hours. For thirty minutes of wetting, enter 0.5 hours rather than 30.

• Use mm/hr for both infiltration capacities.
• Use 1/hr for the decay constant.
• Use hours for time.
• For a standard declining Horton curve, keep f₀ ≥ f_c.

If the appropriate Horton parameters are uncertain, test a plausible range instead of assuming one value is exact. Compare lower, baseline, and higher capacity cases. A result that changes little across that range may support a stable preliminary decision; a result that changes substantially indicates that local infiltration testing or calibration deserves more attention.

Horton infiltration formula used by the calculator

The calculator evaluates Horton’s instantaneous infiltration capacity with the equation below. At time zero, the rate is f₀; as wetting continues, the exponential term causes the rate to approach f_c.

The first calculator output is this Horton expression evaluated at the entered time. It is a rate reported in mm/hr, indicating estimated soil infiltration capacity at that moment rather than the total depth that has entered the soil.

For Horton cumulative infiltration depth from time zero through time t, the calculator integrates the declining capacity curve:

This cumulative Horton result is reported in millimeters. It is the depth that could infiltrate over the full interval if water is continuously available at the soil surface. Horton’s equation describes infiltration capacity, not guaranteed actual infiltration for every rainfall pattern. When rainfall intensity is below the computed capacity, actual infiltration is constrained by rainfall supply because the soil cannot absorb water that is not present at the surface.

Worked example: Horton rate and cumulative depth after two hours

For the default Horton inputs in the form, use f₀ = 75 mm/hr, f_c = 10 mm/hr, k = 0.6 1/hr, and t = 2 hr. The exponential term is e^-1.2, or approximately 0.301. Substituting it into the Horton rate equation gives 10 + (75 - 10) × 0.301, an instantaneous infiltration capacity of about 29.58 mm/hr.

For Horton cumulative infiltration, multiply the final capacity by time and add the integrated decaying term: 10 × 2 + ((75 - 10) / 0.6) × (1 - 0.301). The result is about 95.70 mm. These outputs answer different questions: after two hours the estimated capacity has fallen well below its initial value, while the cumulative total reflects water that could have entered throughout the entire two-hour period.

How to interpret Horton infiltration results in design or field work

This Horton calculator reports two complementary measures. Infiltration rate at time t lets you compare soil intake capacity with rainfall or irrigation intensity at that same moment. If storm intensity exceeds the predicted late-event capacity, the site may begin ponding or producing runoff even if the beginning of the event appeared manageable. Cumulative infiltration, by contrast, is a depth total for the whole modeled interval and is useful for comparing how much water the soil could have accepted during an event or test.

When reviewing Horton results, ask three practical questions. First, is the time basis correct? A value at 0.5 hours represents a different wetting condition than one at 5 hours. Second, do the relative sizes of f₀, f_c, and k resemble the soil behavior expected at the site? Third, when a key parameter changes, does the output respond in the expected direction? Increasing k should make capacity decline faster, while increasing f_c raises the lower portion of the curve.

It is important to separate Horton infiltration capacity from observed infiltration. The equation estimates what the soil can potentially accept while water remains available. It does not automatically represent rainfall gaps, microtopography, run-on from upslope areas, intermittently active macropores, or surface sealing that changes with sediment. That simplification can be suitable for preliminary planning, but parameters should be calibrated against local tests where the result affects a final design or compliance decision.

The copy button can help document Horton scenarios. Calculate one set of soil and duration assumptions, copy the displayed result, change one input, and copy the next result. Keeping those outputs together makes it easier to show how a different storm duration, soil treatment, or parameter assumption changes the estimated capacity and cumulative depth.

Assumptions and limitations of Horton infiltration estimates

Horton infiltration is widely used because the declining-capacity curve is compact and intuitive, but it remains an empirical representation of soil behavior. It reduces field conditions to a smooth decline toward a lower capacity. That can be appropriate for screening calculations, yet it does not replace site investigation. Treat the output as an estimate and compare it with measured behavior when decisions have important consequences.

• Rainfall supply limit: actual infiltration cannot exceed the water available at the surface.
• Surface condition sensitivity: crusting, compaction, tillage, mulch, and sediment can change the curve significantly.
• Spatial variability: one test location may not represent an entire site or field.
• Parameter calibration: f₀, f_c, and k are best taken from local measurements when the result affects design.
• Model form: the standard declining Horton curve assumes infiltration capacity decreases toward a stable lower bound rather than increasing over time.
• Displayed rounding: the page rounds results for readability, so tiny differences from hand calculations are normal.

For Horton infiltration, this calculator is most useful for quick scenario comparisons, educational use, and first-pass runoff reasoning. Its reliability decreases where strong soil layering, preferential flow, or highly variable surface conditions cannot be represented by one declining curve. In those circumstances, use the result as a starting point rather than a final site characterization.