About this calculator
This tool estimates the ultimate and allowable bearing capacity of a shallow footing — strip, square, rectangular, or circular — using the classical Terzaghi (1943) or Meyerhof (1963) bearing-capacity equation, including shape and depth factors and a simplified water-table correction. It is intended for geotechnical and structural engineers doing preliminary shallow-foundation sizing.
Method & formulas
General bearing capacity equation — a superposition of a cohesion term, a surcharge (overburden) term, and a soil self-weight term:
qu = c·Nc·sc(·dc) + q·Nq·sq(·dq) + 0.5·γ·B·Nγ·sγ(·dγ)
c = soil cohesion, q = γ·Df is the effective overburden pressure at the footing base, γ = soil unit weight, B = footing width, and Nc, Nq, Nγ are dimensionless bearing-capacity factors depending only on φ. Terzaghi's (1943) form omits the depth factors d; Meyerhof's (1963) extension includes them.
Bearing capacity factors: Nq and Nc = (Nq − 1)·cotφ follow from classical earth-pressure/slip-surface theory and are tabulated versus φ alone (Nc = 5.7 or π+2 at φ = 0°, depending on the method). Nγ has no closed-form solution and different authors report different values for the same φ; this tool uses the widely-cited approximation Nγ ≈ (Nq − 1)·tan(1.4φ).
Shape factors sc, sq, sγ adjust the strip equation for square, rectangular, or circular footings. Depth factors dc, dq, dγ (Meyerhof only) account for shear resistance mobilized in the soil above the footing base.
Water table correction: where the water table lies at or above the footing base, the submerged unit weight γ′ = γ − γw replaces γ in the self-weight term (and partly the surcharge term).
Allowable pressure: qa = qu / FS (gross); qa,net = (qu − γDf) / FS (net of overburden removed by excavation), typically FS = 2.5–3.0.
Worked example
Terzaghi, square footing: φ=30°, c=10 kPa, γ=18 kN/m³, B=L=2 m, Df=1.5 m, FS=3, no water table.
Factors at φ=30°: Nq≈22.5, Nc≈37.2, Nγ≈19.3. Shape (square): sc=1.3, sγ=0.8.
q = γDf = 27 kPa. Terms: cohesion 10×37.2×1.3≈483 kPa; surcharge 27×22.5≈606 kPa; self-weight 0.5×18×2×19.3×0.8≈278 kPa.
qu ≈ 483+606+278 ≈ 1368 kPa.
qa = 1368/3 ≈ 456 kPa; qa,net = (1368−27)/3 ≈ 447 kPa.
Assumptions & limitations
- Assumes general shear failure of a homogeneous soil under a rigid, level footing with vertical, centric loading; eccentric or inclined loads need separate reduction factors not modeled here.
- Nγ is an approximation — different references (Terzaghi, Meyerhof, Vesic, Hansen) give noticeably different Nγ values for the same φ, so results can vary 10–20% by source.
- The water-table correction is simplified; complex stratigraphy or partial submergence in the failure zone should be checked with a full effective-stress analysis.
- Bearing capacity and settlement are independent limit states — a footing that passes this check can still exceed allowable settlement and must be checked separately.
- Verify results against the governing geotechnical report, applicable code, and a licensed engineer's judgment before use in design.
FAQ
- What's the practical difference between the Terzaghi and Meyerhof methods here?
- Terzaghi's (1943) equation targets a shallow footing on stiff soil under general shear failure; Meyerhof's (1963) extension adds depth factors for shear resistance mobilized above the footing base, generally giving a somewhat higher capacity for embedded footings.
- Why does the cohesion term vanish for cohesionless (sandy) soils?
- With c = 0, the term c·Nc·sc drops to zero regardless of Nc, so a sand's bearing capacity comes entirely from the surcharge and self-weight terms — this is why embedment depth Df matters so much for footings in sand.
- Why is qa,net different from qa?
- qa is the gross allowable pressure at the footing base; qa,net subtracts the overburden pressure (γDf) that existed before excavation, giving the additional pressure the structure can add without exceeding the safety factor — usually the more relevant check for settlement-sensitive designs.