Soil Bearing Capacity: How to Calculate the Load Your Soil Can Carry

Every building, no matter how cleverly engineered above ground, ultimately rests on dirt. The soil beneath a footing has to push back against everything stacked on top of it — the structure, its contents, the wind, the snow — without shearing apart or settling unevenly. How much load that soil can take before it fails is its bearing capacity, and estimating it correctly is one of the foundational tasks of geotechnical engineering. Underestimate it and you waste money on oversized foundations; overestimate it and the building tilts, cracks, or worse. This guide walks through Terzaghi's classic bearing-capacity equation, the standard first tool for the job, with a worked example and the safety considerations that turn a raw number into a usable design value.

What Bearing Capacity Is and Why It Matters

Bearing capacity is the maximum pressure soil can support at the base of a foundation before it fails in shear. Two related numbers come up constantly. The ultimate bearing capacity is the theoretical pressure at which the soil collapses. The allowable bearing capacity is that ultimate value divided by a safety factor — the pressure you actually design to.

The distinction is not academic. Soil failure is rarely a clean collapse; far more often it shows up as differential settlement, where one part of a foundation sinks more than another, racking door frames, cracking walls, and stressing the structure in ways it was never meant to take. A sound bearing-capacity estimate sizes footings so that the soil stays comfortably within its safe range under every expected load.

It matters because the cost and safety of a project hinge on it. A footing sized for weak soil is wide and expensive; the same footing on strong rock could be a fraction of the size. Knowing what the ground can carry lets an engineer match the foundation to the site instead of guessing.

The Three Mechanisms Behind Terzaghi's Equation

Karl Terzaghi, the founder of modern soil mechanics, showed that a footing's ultimate capacity comes from three sources, each tied to a property of the soil:

Cohesion — the soil's intrinsic "stickiness," dominant in clays. Captured by a cohesion term scaled by a bearing-capacity factor.
Surcharge — the weight of soil already sitting beside the footing at its founding depth, which helps confine the failure wedge. Captured by a depth-and-unit-weight term.
Self-weight of the failure wedge — the friction the footing mobilizes within the soil mass below it, dominant in sands and gravels. Captured by a term involving the soil's unit weight and footing geometry.

Three dimensionless bearing-capacity factors — conventionally written Nc, Nq, and Nγ — translate the soil's friction angle into how much each mechanism contributes. They rise steeply as the friction angle increases, which is why dense, granular soils carry so much more than soft clays.

How to Calculate the Ultimate Bearing Capacity

For a square footing, Terzaghi's general equation combines the three contributions. In plain terms:

Ultimate Capacity = 1.3 · c · Nc + γ · D · Nq + 0.4 · γ · B · Nγ

where c is cohesion, γ is the soil's unit weight, D is the founding depth, B is the footing width, and Nc, Nq, Nγ are the bearing-capacity factors derived from the friction angle φ. The 1.3 and 0.4 are shape factors specific to square footings. The factors themselves come from φ: as the friction angle grows, Nq and Nγ climb sharply, so the equation rewards stronger, more frictional soils.

Worked example. Consider a square footing founded in a sandy soil:

Cohesion c = 10 kPa
Friction angle φ = 30°
Unit weight γ = 18 kN/m³
Founding depth D = 1.5 m

For φ = 30°, the standard Terzaghi factors are approximately Nc ≈ 37.2, Nq ≈ 22.5, and Nγ ≈ 19.7. (These follow from the friction angle through Terzaghi's expressions and are also tabulated in any geotechnical reference.)

1. Cohesion term: 1.3 × 10 × 37.2 ≈ 484 kPa

2. Surcharge term: 18 × 1.5 × 22.5 ≈ 608 kPa

3. Self-weight term (taking width B = 1.5 m): 0.4 × 18 × 1.5 × 19.7 ≈ 213 kPa

4. Sum: 484 + 608 + 213 ≈ 1,305 kPa ultimate bearing capacity

You can run any combination of cohesion, friction angle, unit weight, and depth instantly with the Soil Bearing Capacity calculator instead of looking up factors and chaining the arithmetic by hand.

From Ultimate Capacity to a Safe Design

The ultimate value is never used directly. Apply a factor of safety — typically 2.5 to 3.0 for shallow foundations — to get the allowable bearing capacity. In the example, 1,305 ÷ 3 ≈ 435 kPa is the pressure you would actually design the footing to carry. That margin absorbs uncertainty in the soil properties, variation across the site, and the consequences of unexpected loads.

A few cautions keep the result honest. Garbage in, garbage out: the answer is only as good as the cohesion and friction angle you feed it, which should come from proper site investigation and lab testing, not assumptions. Check settlement too — a soil can be strong enough against shear failure yet still settle more than the structure tolerates, so bearing capacity and settlement are separate checks. Watch the water table, which reduces the effective unit weight and can sharply cut capacity. And remember that Terzaghi's general equation assumes a shallow footing where depth is no greater than width; deep foundations need different methods. Treat the computed number as a first-pass estimate to be confirmed by a qualified geotechnical engineer, never as a final design on its own.

Conclusion

Soil bearing capacity is where structural ambition meets the limits of the ground. Terzaghi's equation distills a complex failure into three understandable contributions — cohesion, surcharge, and the soil's own friction — and combines them into a single ultimate pressure. Divide that by a sensible safety factor, verify it against settlement, and base the inputs on real testing, and you have a defensible foundation design. Skip those steps and the most beautiful structure in the world still sits on a guess.

Key Takeaways

• Three mechanisms add up: Terzaghi's equation sums cohesion, surcharge, and soil self-weight, each scaled by a bearing-capacity factor driven by the friction angle

• Apply a safety factor: Divide the ultimate capacity by 2.5–3.0 to get the allowable bearing pressure you actually design to

• Inputs decide accuracy: Use cohesion, friction angle, and unit weight from real site investigation with the Soil Bearing Capacity calculator — assumptions produce unreliable results

• Check settlement and water: Adequate shear capacity does not guarantee acceptable settlement, and a high water table can sharply reduce capacity