What this calculator does
Before a footing is poured, someone has to say what pressure the ground can take. This calculator applies the Terzaghi equation with the standard capacity factors and divides by your safety factor, giving an allowable bearing pressure to compare against the structural load.
How to use it
- Enter the footing width and length; for a square footing leave them equal.
- Enter the embedment depth and the soil unit weight, cohesion and friction angle from your investigation.
- Select the footing shape, which changes both the cohesion and the weight term.
- Set the groundwater depth — if it is at or below the footing base the full unit weight applies to the weight term.
Governing formula
qu = c·Nc·sc + q·Nq + ½·γ·B·Nγ·sγ Where:
-
c= Undrained or effective cohesion [kPa] -
q= Surcharge at the footing base [kPa] -
B= Footing width [m]
Derived Equations:
Nq = e^(π tan φ) · tan²(45 + φ/2) Nc = (Nq − 1)/tan φ Nγ ≈ 2(Nq + 1) tan φ q_all = qu / FS Worked example — 2 × 2 m footing in c = 10 kPa, φ = 30° soil
The figures below were produced by running this page's own engine with the example inputs (Footing width (m), Footing length (m), Embedment depth (m), Soil unit weight (kN/m³), Friction angle (°), Cohesion (kPa), Groundwater depth below surface (m), Footing shape, Global safety factor (–)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Allowable bearing pressure | 304.38 kPa |
|---|---|
| Net ultimate pressure | 902.34 kPa |
| Nc (cohesion factor) | 30.14 |
| Nq (surcharge factor) | 18.4 |
| Nγ (weight factor) | 22.4 |
| Shape | Square |
| Assessment | Terzaghi general shear: qu 913 kPa (allowable 304 kPa at FS 3). Verify with site-specific soil parameters and apply against a known critical failure plane. |
- At φ = 30° the factors are Nc ≈ 19.4, Nq ≈ 18.4 and Nγ ≈ 22.5.
- The cohesion term dominates because c is high: 10 × 19.4 × 1.3 ≈ 252 kPa.
- After the weight and surcharge terms, dividing by a factor of safety of 3 gives an allowable pressure to compare against the wall load.
Assumptions & limitations
Engineering calculation. Terzaghi general-shear bearing capacity with the classical shape factors. No depth, inclination or seismic factors, and no consolidation settlement check.
- Terzaghi assumes a shallow, rigid foundation on homogeneous soil with general shear failure; deep footings, rock, highly anisotropic soil or near-failure conditions need other methods.
- Uses effective or total stress parameters inconsistently if the groundwater table is high — take care to match the parameters to the drainage condition.
- Settlement frequently governs before bearing does; check it with the settlement calculator in the same cluster.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- Terzaghi (1943) — theoretical analysis of the bearing capacity of soils.
- BS EN 1997-1 — bearing capacity and bearing resistance.
- Das, Principles of Foundation Engineering.