Soil Bearing Capacity: How to Calculate the Load Your Soil Can Carry
The soil beneath a footing has to carry everything stacked on it without shearing or settling unevenly. The pressure at which it fails is its bearing capacity, and estimating it is one of the first tasks in foundation design: underestimate it and the footings are oversized and expensive; overestimate it and the building tilts or cracks. This guide walks through Terzaghi's bearing-capacity equation as the Soil Bearing Capacity Calculator applies it, with a worked example and the safety factor that turns the raw number into a 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.
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 for square footings; a strip footing uses 1.0 and 0.5.
The factors are where published tables differ. Terzaghi's original 1943 factors (for φ = 30°: Nc ≈ 37.2, Nq ≈ 22.5, Nγ ≈ 19.7) are still printed in many textbooks. The calculator instead uses the closed-form expressions in general use today: Nq = e^(π·tan φ) · tan²(45° + φ/2), Nc = (Nq − 1) ÷ tan φ (5.14 for φ = 0) and Brinch Hansen's Nγ = 1.5 (Nq − 1) tan φ. These give lower, more conservative values than Terzaghi's originals; for φ = 30° they are Nq = 18.40, Nc = 30.14 and Nγ = 15.07. All three climb steeply with φ, so the equation rewards dense, frictional soils.
Worked example. Consider a square footing in a sandy soil:
- Cohesion c = 10 kPa
- Friction angle φ = 30°
- Unit weight γ = 18 kN/m³
- Founding depth D = 1.5 m
- Footing width B = 1.5 m
1. Cohesion term: 1.3 × 10 × 30.14 = 391.8 kPa
2. Surcharge term: 18 × 1.5 × 18.40 = 496.8 kPa
3. Self-weight term: 0.4 × 18 × 1.5 × 15.07 = 162.8 kPa
4. Sum: 391.8 + 496.8 + 162.8 ≈ 1,051 kPa ultimate bearing capacity
Entering the same five values into the Soil Bearing Capacity Calculator gives the same result. With Terzaghi's original factors the sum would be about 1,305 kPa, which shows how much the choice of factor table matters and why the design value must be read with a safety factor.
From Ultimate Capacity to a Safe Design
The ultimate value is never used directly. Apply a factor of safety, typically 3 for general shear failure and 2.5 for local shear, to get the allowable bearing capacity. In the example, 1,051 ÷ 3 ≈ 350 kPa is the pressure you would design the footing to carry; on a 1.5 m × 1.5 m footing that is a column load of about 350 × 2.25 ≈ 790 kN before any settlement check. That margin absorbs uncertainty in the soil properties, variation across the site and 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, not engineering advice; a licensed geotechnical engineer must confirm any design value.
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; the example's 1,051 kPa becomes about 350 kPa
• Inputs and factors decide accuracy: Use cohesion, friction angle and unit weight from real site investigation, and know which factor table you are using (the calculator's closed-form factors run below Terzaghi's originals)
• Check settlement and water: Adequate shear capacity does not guarantee acceptable settlement, and a high water table can sharply reduce capacity