Soil Bearing Capacity Calculator

Introduction

When a building load reaches the ground through a footing, the soil has to resist that pressure without shearing and without settling so much that the structure becomes unsafe. That simple idea is what engineers mean by soil bearing capacity. If the applied pressure is too high for the supporting soil, the footing can punch into the ground, tilt, or settle unevenly. Even when outright failure never occurs, excessive settlement can crack walls, jam doors, distort slabs, and create long-term service problems. Because of that, bearing-capacity checks are one of the first screening calculations in shallow foundation design.

This calculator estimates the capacity of soil beneath a shallow strip footing by using Terzaghi's classic bearing-capacity theory. The tool combines footing width, embedment depth, unit weight, cohesion, friction angle, and a factor of safety to produce two practical outputs: the ultimate bearing capacity and the net allowable bearing capacity. Ultimate capacity is the theoretical pressure at failure according to the model. Net allowable capacity is the more usable planning number, because it includes a safety reduction and subtracts the surcharge from the soil above the footing base.

Used correctly, this type of calculator is very helpful during preliminary design, conceptual estimating, classroom study, and quick scenario testing. It shows how a wider footing spreads load, how stronger soil raises capacity, and how a deeper founding level can increase confinement. At the same time, no browser calculator can replace a geotechnical report or a licensed design review. Real foundations are influenced by settlement limits, groundwater, stratified soils, nearby excavations, seismic effects, and local code requirements. Treat the result as a fast engineering estimate, then confirm the final design with site-specific data.

How to Use the Calculator

Start with the footing geometry. Enter the footing width in meters and the embedment depth measured from the ground surface to the base of the footing. For a strip footing, width is the dimension that spreads the load across the soil. A larger width usually lowers the contact pressure from the structure and increases the width term in Terzaghi's equation. Embedment depth matters because the soil above the footing base creates surcharge pressure, which can improve resistance against bearing failure.

Next, enter the soil parameters. Unit weight is the bulk weight of soil in kilonewtons per cubic meter. Cohesion describes the part of soil strength that does not depend on normal pressure, which is often important in clays. Friction angle describes the internal shearing resistance that becomes more significant in sands and granular soils. In this page's current calculator logic, every field must contain a positive number. If you want to represent a practically cohesionless sand, enter a very small positive cohesion value such as 0.1 kPa instead of zero, then interpret the result accordingly.

Finally, choose a factor of safety. This is the step that turns a theoretical failure pressure into a more conservative working value. A factor of safety near 3 is common for preliminary shallow foundation checks, but your project may require a different value based on code, load uncertainty, or the quality of the site investigation. After you press Compute Capacity, the result panel shows the ultimate capacity and the net allowable capacity in kilopascals. The Copy Result button lets you move those values into notes, estimates, or project correspondence.

What the Inputs Mean

The calculator is easiest to trust when each field has a clear physical meaning. These inputs work together, so a small change in one variable can noticeably affect the final answer.

• Footing Width (m): the strip footing width B. A wider footing distributes the same structural load over more soil and changes the unit-weight contribution in the bearing-capacity equation.
• Embedment Depth (m): the depth D from the ground surface to the footing base. Greater depth increases surcharge, represented by the term gamma times depth.
• Unit Weight (kN/m³): the soil unit weight. Heavier soil creates more surcharge but also affects the width-related contribution to ultimate capacity.
• Cohesion (kPa): the cohesive strength, often important in clays or partly cemented soils.
• Friction Angle (°): the angle that governs the bearing-capacity factors for frictional resistance.
• Factor of Safety: a reduction applied to ultimate capacity so the reported working value includes a margin against uncertainty.

The unit system here is internally consistent: width and depth are in meters, unit weight is in kilonewtons per cubic meter, and cohesion is in kilopascals. Because one kilopascal equals one kilonewton per square meter, the final bearing capacities naturally appear in kPa. If your source data is in pounds per square foot, tons per square foot, or feet, convert it before entering values.

Terzaghi's Formula in Detail

Terzaghi's method breaks ultimate bearing capacity into three contributions. One comes from cohesion, one comes from the surcharge of soil above the footing base, and one comes from the weight of soil mobilized beneath the footing. The three bearing-capacity factors, $N_c$, $N_q$, and $N_{\gamma }$, depend only on the soil friction angle $\phi$. Those factors are shown below in MathML so the formulas remain machine-readable as well as human-readable.

The ultimate bearing capacity for a strip footing of width $B$ embedded at depth $D$ is then:

Where $c$ is the soil cohesion, $\gamma$ is the soil unit weight, and $D$ is the footing base depth below the ground surface. Dividing the ultimate capacity by a factor of safety gives a working pressure, and subtracting the surcharge term $\gamma D$ yields the net allowable value that is often compared with service loading.

The calculator also reports the net allowable bearing capacity $q_a$, using the relationship below:

In plain language, the formula says this: stronger soil and a more favorable footing geometry produce a larger failure pressure, but the design should never use that full theoretical limit as the working load. The factor of safety is what turns the raw equation into a cautious design check. That is why the net allowable result is usually the number compared with service-level foundation pressure during early sizing.

How the Result Should Be Read

The result panel reports two values because they answer slightly different questions. Ultimate capacity tells you what the idealized Terzaghi model predicts at failure. It is useful for understanding the mechanics of the soil and for seeing how sensitive the site is to changes in cohesion, friction angle, or depth. Net allowable capacity is the more practical screening number. It tells you how much net pressure the footing should be allowed to transmit after applying the selected factor of safety and after accounting for the soil surcharge above the footing base.

A quick first-pass service-pressure comparison can be written as:

If you want a simple reserve measure, you can think of adequacy as the ratio below. Values greater than 1 mean the reported allowable capacity is larger than the estimated service pressure:

To interpret the number, compare your anticipated service pressure from the structure to the net allowable capacity. If the building load divided by the footing area is comfortably below the reported net allowable value, the footing may be adequate from a bearing-capacity perspective. If it is close to or above the reported value, you may need to widen the footing, lower the load, improve the soil, increase embedment, or shift to a different foundation system. A good engineering habit is to leave margin, not to design exactly on the edge.

Worked Example

Suppose you are checking a 1.0 m wide strip footing founded 1.5 m below grade in dense sand. Use a unit weight of 18 kN/m³, a very small cohesion of 0.1 kPa to approximate a nearly cohesionless soil in this specific calculator, a friction angle of 35°, and a factor of safety of 3. The bearing-capacity factors become large because a 35° friction angle creates strong frictional resistance. Using the equation above gives an ultimate capacity on the order of about 646 kPa, with the exact value depending on rounding.

Divide that value by the factor of safety and then subtract the surcharge term from the overlying soil. The resulting net allowable capacity is roughly 188 kPa. If your estimated service contact pressure from the structure is only 140 kPa, the footing looks reasonable in a first-pass check. If the service pressure is 220 kPa, the footing is too heavily loaded for the assumed conditions and would need revision. That is the kind of quick design judgment this calculator is intended to support: it does not replace a full geotechnical design, but it makes tradeoffs visible immediately.

Assumptions and Limitations

Terzaghi's original shallow-foundation theory is a classic starting point, but it is still a simplified model. It assumes a strip footing on level ground resting on homogeneous soil. It does not automatically include footing shape factors, base inclination, load eccentricity, sloping ground, layered soil profiles, or the many corrections used in more advanced methods. Groundwater can materially change effective unit weight and therefore alter both the surcharge and unit-weight terms. If the water table is high, the true bearing capacity may be lower than a dry-soil estimate suggests.

Another important limitation is that bearing failure is not the only design criterion. Many foundations are governed by settlement rather than by ultimate shear failure. A footing may have enough nominal bearing capacity and still settle too much for the building it supports. Soft clays, loose fills, collapsible soils, and variable strata are common reasons why a formal geotechnical investigation is worth the time. Use this calculator to understand trends and build intuition, but rely on project-specific recommendations for final dimensions.

Practical Design Notes

If the allowable value comes out lower than expected, the first and simplest change is often to increase footing width. A wider footing spreads the same load over a larger area and usually lowers the applied contact pressure. Increasing embedment depth can also help, although excavation cost, frost depth, drainage, and adjacent structures may limit how deep it is practical to go. In some cases, the right answer is not a wider shallow footing at all, but ground improvement, a mat foundation, or deep foundations bearing on stronger material below.

It is also worth checking your inputs with care. Friction angle and cohesion should come from appropriate testing or from reliable geotechnical correlations, not from guesswork. Unit weight should reflect the field condition that matters most for design. Finally, remember that the factor of safety expresses uncertainty. When soil data is sparse, construction quality is variable, or the consequences of movement are serious, conservative assumptions are justified. This calculator makes experimentation easy because it runs entirely in your browser, so you can compare several what-if cases before moving on to a more formal design step.

Recording Your Capacity Study

Once the capacities appear, you can use the copy button to store the values in your estimate, field note, or design worksheet. Keeping a brief record of the assumed width, depth, soil parameters, and factor of safety is useful later when you compare alternate footing sizes or explain why a layout changed during design development. Even for small projects, that simple record improves transparency and helps prevent unit mistakes or undocumented assumptions.

One useful habit is to record not only the final answer but also the range of answers produced by a few realistic scenarios. Try one conservative case, one expected case, and one optimistic case. That small sensitivity study often reveals whether footing width, friction angle, or groundwater assumptions are driving the result. If one small change produces a very large shift in net allowable pressure, that is a sign the design deserves closer site investigation before decisions become expensive.