Horton Infiltration Rate Calculator

How Horton infiltration estimates help you read a storm

Soil does not usually accept water at one constant rate from the first minute of rainfall to the last. A dry surface often takes in water quickly at the beginning of a storm, then slows as the upper soil wets, pore spaces fill, and surface sealing or compaction begins to matter. Horton’s infiltration equation captures that familiar pattern with a declining curve: the rate starts near an initial capacity, then gradually approaches a lower long-run capacity. This calculator turns that curve into two practical results you can use immediately: the infiltration capacity at a chosen time and the cumulative depth that could infiltrate over the same period.

That distinction is important in drainage, irrigation, erosion control, and simple runoff screening. If rainfall intensity stays below the soil’s infiltration capacity, water can continue moving into the ground without ponding. If rainfall intensity rises above that capacity, the excess becomes available for surface storage or runoff. A single number is not enough to describe that change, because the soil response at the start of wetting is often very different from the response later in the event. Horton’s model gives you a compact way to estimate both the changing rate and the running total.

This page is written to help you do more than press a button. The sections below explain what each input represents, why the units matter, how the formula works, and how to interpret the results in plain language. If you are comparing site conditions, testing irrigation durations, or checking whether a storm might outpace soil intake, this calculator gives you a quick first-pass estimate before you move on to field calibration or a more detailed hydrologic model.

What the four inputs mean in practice

The Horton equation needs four inputs: an initial infiltration capacity f₀, a final infiltration capacity f_c, a decay constant k, and elapsed time t. Each one has a physical interpretation. Together they describe how quickly the soil starts, where it settles, how fast it drops, and how long the wetting has continued.

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 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 curve at that selected moment, then also computes the cumulative infiltrated depth from time zero to that same point.

Most input mistakes come from unit mismatches rather than algebra. If your field notes are in minutes but you leave k in 1/hr, the result will be off even though the formula is coded correctly. Keep the rate terms in mm/hr, keep k in 1/hr, and enter time in hours. If you have 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 you are uncertain about the right values, scenario testing is more honest than pretending there is only one perfect answer. Run a conservative case, a baseline case, and an optimistic case. If the result changes only a little across that range, your decision may be robust. If the result swings widely, that is a sign that field measurement or calibration deserves more attention.

Formula used by the calculator

Horton’s instantaneous infiltration capacity is shown below. It begins at f₀ when time is zero and then decays exponentially toward f_c.

The first output of the calculator is simply that expression evaluated at your chosen time. The result is a rate, so it is reported in mm/hr. That value tells you the soil’s estimated infiltration capacity at that moment, not the total depth infiltrated so far.

To find the cumulative depth from time zero to time t, the calculator integrates the infiltration-rate curve. That gives the second formula:

This cumulative result is reported in millimeters. It represents the depth that could infiltrate over the full interval if water is continuously available at the soil surface. That last phrase matters. Horton’s equation describes infiltration capacity, not guaranteed actual infiltration under every rainfall pattern. If rainfall intensity is lower than the computed capacity, then actual infiltration is limited by the rainfall supply. In other words, the soil cannot absorb more water than is physically present at the surface.

Worked example

Suppose you enter the default values shown in the form: f₀ = 75 mm/hr, f_c = 10 mm/hr, k = 0.6 1/hr, and t = 2 hr. First calculate the exponential term: e^-1.2, which is about 0.301. Substituting that into Horton’s equation gives an instantaneous capacity of 10 + (75 - 10) × 0.301, or about 29.58 mm/hr.

For the cumulative depth, multiply the final capacity by time and then add the integrated decaying term: 10 × 2 + ((75 - 10) / 0.6) × (1 - 0.301). That yields about 95.70 mm. Read those two outputs together. After two hours, the soil is no longer taking in water as fast as it did at the beginning, but it may still have accepted a substantial total depth over the whole period. That is why the cumulative value can be large even while the instantaneous rate has already dropped sharply.

How to interpret the result in a design or field context

The result area reports two different but complementary measures. The infiltration rate at time t helps you compare soil intake with a rainfall or irrigation intensity at that same moment. If the storm intensity exceeds the predicted infiltration capacity late in the event, the site may begin ponding or producing runoff even if the opening minutes looked comfortable. The cumulative infiltration result, by contrast, is a depth total. It is useful when you want to compare how much water the soil could have accepted over the whole event or test period.

A simple interpretation pattern is to ask three questions. First, is the time basis correct? A value computed at 0.5 hours means something very different from one computed at 5 hours. Second, does the relative size of f₀, f_c, and k match the soil behavior you expect? Third, if you increase or decrease one key parameter, does the result move in the direction hydrology suggests? For example, increasing k should make the rate drop faster, and increasing f_c should raise the tail end of the curve.

It is also worth separating capacity from observed infiltration. Horton’s equation says how much the soil can potentially accept under a continuing water supply. It does not automatically include rainfall gaps, microtopography, run-on from upslope areas, macropores that activate intermittently, or changing surface sealing from sediment. In preliminary planning, that is usually acceptable. In final design or compliance work, it is a reminder to calibrate the parameters against local tests whenever possible.

The copy button below the calculator is handy when you are comparing several scenarios. Run one case, copy the result, adjust a single input, and copy the next result. That workflow makes it easier to document assumptions and explain why one design storm, irrigation duration, or soil treatment looks more favorable than another.

Assumptions and limitations

Horton’s equation is widely used because it is compact and intuitive, but it is still an empirical model. It simplifies field conditions into a smooth declining curve. That is often exactly what you need for screening calculations, yet it is not a substitute for site investigation. Use the output as an estimate that should be checked against measured behavior when decisions become consequential.

• 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.

As a rule of thumb, this calculator is excellent for quick scenario comparison, educational use, and first-pass runoff thinking. It becomes less reliable when the site has strong layering, preferential flow, or highly variable surface conditions that a single declining curve cannot represent well. In those cases, treat the result as a starting point and not the last word.