Soil Bearing Capacity Calculator
Calculate the ultimate and allowable bearing capacity of a strip, square or circular shallow footing with Terzaghi’s equation from cohesion, friction angle, unit weight, width, depth and factor of safety.
How it works
strip: qu = c·Nc + q·Nq + 0.5·γ·B·Nγ · square: qu = 1.3·c·Nc + q·Nq + 0.4·γ·B·Nγ · circular: qu = 1.3·c·Nc + q·Nq + 0.3·γ·B·Nγ · q = γ·Df · Nq = e^(2(3π/4 − φ/2)tanφ) ÷ (2cos²(45° + φ/2)) · Nc = (Nq − 1)·cotφ · qa = qu ÷ FS
Terzaghi’s 1943 bearing capacity theory adds three resistances of a shallow footing (depth no greater than its width): soil cohesion, the surcharge of soil above the base, and the friction of the soil wedge under the footing. The factors Nc and Nq follow from the friction angle φ by closed formulas and Nγ is taken from the standard table (Das, Principles of Foundation Engineering, Table 4.1), interpolated between 5° steps. Shape factors 1.3, 0.4 and 0.3 adapt the strip equation to square and circular footings. Dividing by a factor of safety of about 3 gives the allowable pressure. The equation assumes general shear failure, a water table well below the footing and no settlement limit; a high water table roughly halves the γ terms.
Worked example
A 1.5 m square footing 1.0 m deep in soil with c = 10 kPa, φ = 30° and γ = 18 kN/m³: Nc = 37.16, Nq = 22.46, Nγ = 19.13 and q = 18 × 1.0 = 18 kPa. qu = 1.3 × 10 × 37.16 + 18 × 22.46 + 0.4 × 18 × 1.5 × 19.13 = 483 + 404 + 207 = 1,094 kPa. With FS = 3, qa = 365 kPa (3.72 kg/cm²), so the footing can carry about 365 × 1.5² = 820 kN (84 t).
Sources: Das, B. M. — Principles of Foundation Engineering (Terzaghi bearing capacity, Table 4.1) · FHWA NHI-06-089 Soils and Foundations Reference Manual, Vol. II (bearing capacity)
Frequently asked questions
What is the difference between ultimate and allowable bearing capacity?
Ultimate bearing capacity is the pressure at which the soil fails in shear. Allowable bearing capacity divides it by a factor of safety, usually 2.5–3, and in practice is also limited by acceptable settlement.
What are typical allowable bearing pressures?
Rough presumptive values (e.g. IBC Table 1806.2): soft clay 75–100 kPa (1,500–2,000 psf), stiff clay and silty sand 150–200 kPa, dense sand and gravel 200–300 kPa, and sound rock far more. Always confirm with a soil study.
How do I convert kPa to kg/cm²?
Divide by 98.07: 100 kPa ≈ 1.02 kg/cm² ≈ 2,089 psf. A soil report quoting 2 kg/cm² means about 196 kPa.
How does the water table affect bearing capacity?
Below the water table soil weighs only its submerged (buoyant) weight, roughly half, so the q and γ terms drop sharply. If water is near the footing base, use the submerged unit weight (about 8–10 kN/m³).
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Foundation design must be based on a site soil investigation and checked by a qualified geotechnical or structural engineer.