Soil Bearing Capacity Calculator
Three Separate Failure Mechanisms, Added Together
Terzaghi's 1943 bearing capacity theory treats a foundation's ultimate capacity as the sum of three independent contributions: the soil's cohesion, the surcharge pressure from soil above the footing, and the weight of soil within the failure wedge below it. Each contribution is scaled by a bearing capacity factor — Nc, Nq, and Nγ — that depends entirely on the soil's friction angle, and the shape of the footing further adjusts the cohesion and weight terms.
The Formulas
Strip footing: qu = c × Nc + q × Nq + 0.5 × γ × B × Nγ
Square footing: qu = 1.3 × c × Nc + q × Nq + 0.4 × γ × B × Nγ
Circular footing: qu = 1.3 × c × Nc + q × Nq + 0.3 × γ × B × Nγ
q (surcharge) = γ × Df
Allowable Bearing Capacity = qu / Factor of Safety
Square footing: qu = 1.3 × c × Nc + q × Nq + 0.4 × γ × B × Nγ
Circular footing: qu = 1.3 × c × Nc + q × Nq + 0.3 × γ × B × Nγ
q (surcharge) = γ × Df
Allowable Bearing Capacity = qu / Factor of Safety
Bearing Capacity Factors by Friction Angle
| Friction angle (φ) | Nc | Nq | Nγ |
|---|---|---|---|
| 0° | 5.70 | 1.00 | 0.00 |
| 20° | 17.69 | 7.44 | 0.24 |
| 25° | 25.13 | 12.72 | 0.47 |
| 30° | 37.16 | 22.46 | 0.87 |
| 35° | 57.75 | 41.44 | 1.58 |
| 40° | 95.66 | 81.27 | 2.87 |
Note: the Nc and Nq values above match Terzaghi's widely published 1943 general-shear table closely (for example, Nc ≈ 37.2 and Nq ≈ 22.5 at φ = 30°). The Nγ values from this calculator's closed-form formula are noticeably lower than the Nγ figures in most published Terzaghi or Vesic tables (commonly around 15–20 at φ = 30°), so for foundations where the weight term contributes significantly to capacity — wide footings on granular soil in particular — cross-check Nγ against a professional geotechnical reference table.
Worked Example: Strip Footing
| Quantity | Value |
|---|---|
| Surcharge q | 18 kPa |
| Ultimate bearing capacity qu | 415.90 kPa |
| Allowable bearing capacity (qu / 3) | 138.63 kPa |
Where This Gets Used
- Sizing a shallow foundation — checking whether a proposed footing width keeps bearing pressure under the allowable capacity for the given soil.
- Comparing footing shapes — the shape correction factors on the cohesion and weight terms mean a square or circular footing behaves differently than a strip footing of the same width.
- Early geotechnical screening — a quick estimate before a full site-specific geotechnical investigation and design.
How to Use This Calculator
- Choose Unit system and Footing Shape — Strip, Square, or Circular.
- Enter Cohesion c, Soil Unit Weight, Friction Angle phi (0–45 degrees), Footing Width B, and Footing Depth Df.
- Enter Factor of Safety (defaults to 3 if left blank).
- Select Calculate to see the ultimate and allowable bearing capacity.
Note: this is a shallow-foundation, general-shear estimate and does not account for the water table, load eccentricity, or local/punching shear.
Related Calculations
Check the load this footing needs to carry with the Structural Load Calculator, or evaluate a nearby cut slope with the Slope Stability Calculator.