Soil Bearing Capacity Calculator
Estimate the ultimate bearing capacity of soil beneath a square footing using Terzaghi's general bearing-capacity equation. Foundational geotechnical design input — used with appropriate safety factors to determine maximum allowable footing loads.
Last updated: May 2026
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About this calculator
Terzaghi's general bearing-capacity equation for a square footing is q_u = 1.3·c·N_c + γ·D_f·N_q + 0.4·γ·B·N_γ, where q_u is ultimate bearing capacity (kPa), c is soil cohesion (kPa), γ is unit weight of soil (kN/m³), D_f is footing depth below ground surface (m), B is footing width (m), and N_c, N_q, N_γ are dimensionless bearing-capacity factors that depend on the soil's internal friction angle φ. The three terms represent contributions from cohesion, surcharge from soil above the footing base, and the friction-strength contribution from the soil below. Bearing-capacity factors follow standard formulas: N_q = e^(π·tan φ)·tan²(45° + φ/2); N_c = (N_q − 1) / tan φ (with a limit for φ = 0); N_γ ≈ 2(N_q + 1)·tan φ (Brinch Hansen approximation). For clays (φ = 0, undrained): N_c = 5.14, N_q = 1, N_γ = 0; for granular soils (sand, φ > 0): all three contribute. Variables: c = cohesion (significant for clays, zero for clean sands), φ = internal friction angle (0° for soft clay, 25°–35° for typical sand, 40°+ for dense gravels), γ = unit weight (~17–20 kN/m³ for typical soils), B = footing width, D_f = depth. Edge cases: ultimate capacity must be divided by a safety factor (typically 2.5–3.0) to get allowable bearing pressure. For non-square footings, use Meyerhof or Hansen shape factors. Layered soils require separate analysis; groundwater above the footing reduces effective γ to buoyant unit weight γ' ≈ γ − 10 kN/m³. The simple Terzaghi formula assumes general shear failure (stiff soils); local or punching shear failure modes in loose soils require reduced bearing-capacity factors.
How to use
Example 1 — Square footing in clay. A 2.0 m × 2.0 m square footing at D_f = 1.5 m depth in stiff clay with c = 60 kPa, φ = 0°, γ = 18 kN/m³. For φ = 0: N_c = 5.14, N_q = 1, N_γ = 0. q_u = 1.3 × 60 × 5.14 + 18 × 1.5 × 1 + 0.4 × 18 × 2.0 × 0 = 400.9 + 27 + 0 = 427.9 kPa. ✓ Apply safety factor 3.0: q_allow = 427.9 / 3.0 ≈ 143 kPa. With B² = 4 m² footing area, the maximum allowable column load is 143 × 4 = 572 kN. Example 2 — Square footing in sand. 1.5 m × 1.5 m footing at D_f = 1.0 m in medium-dense sand with c = 0, φ = 32°, γ = 19 kN/m³. Compute bearing factors: tan(32°) = 0.625; N_q = e^(π × 0.625) × tan²(61°) = e^1.963 × 3.255 ≈ 7.12 × 3.255 ≈ 23.18; N_γ ≈ 2 × (23.18 + 1) × 0.625 ≈ 30.23. q_u = 1.3 × 0 × N_c + 19 × 1.0 × 23.18 + 0.4 × 19 × 1.5 × 30.23 = 0 + 440.4 + 344.6 ≈ 785 kPa. ✓ Apply safety factor 3.0: q_allow = 785/3 ≈ 262 kPa. The maximum allowable column load on this footing is 262 × 1.5² ≈ 588 kN.
Frequently asked questions
What is a safe bearing-capacity factor of safety?
Geotechnical practice typically uses a factor of safety (FoS) between 2.5 and 3.0 against ultimate bearing capacity. FoS = 3.0 is common for routine shallow foundations on soils without detailed site investigation; FoS = 2.5 is acceptable when soil parameters are well-characterised from extensive testing; FoS = 2.0 is permitted for some temporary works or seismic load combinations. The high factor accounts for natural soil variability (test results can vary ±30% from spot to spot), uncertainty in load distribution, settlement considerations (which often govern before bearing capacity does), and the consequences of foundation failure (sudden, catastrophic, with no warning in punching-shear modes). Eurocode 7 uses partial factors on soil parameters rather than a single overall FoS, leading to similar but more transparent results. Allowable bearing pressure is q_allow = q_u / FoS, and is what's used in design.
How does footing depth affect bearing capacity?
Deeper footings have higher bearing capacity for two reasons. First, the surcharge term (γ·D_f·N_q) grows linearly with depth — overburden weight above the footing base acts as a confining pressure that increases the soil's strength against shear failure. Second, the soil at depth is typically denser and stronger than near-surface soil (which has been disturbed by weather, vegetation, and construction). At D_f = 0 (footing on the surface) the surcharge term vanishes; at D_f = 2B (deep footing) the surcharge can dominate the bearing equation. For deep foundations (piles), the formula changes entirely — pile capacity comes from a different mechanism (skin friction along the shaft plus end bearing). Most shallow footings sit at D_f = 0.5–2.0 m below grade, deep enough to be below the active zone (frost, drying, vegetation roots) but shallow enough for cost-effective excavation.
What's the difference between general shear, local shear, and punching shear failure?
General shear failure occurs in stiff, dense soils — a clear failure surface develops and the footing settles suddenly with a heave at the surface around it. The full Terzaghi capacity formula applies. Local shear failure occurs in soils of intermediate density — partial failure surface develops, but heave is not visible at the surface; reduce the bearing-capacity factors to about 2/3 of their general-shear values. Punching shear failure occurs in loose, soft soils — the footing punches downward without forming a clear lateral failure surface; this is the most dangerous mode because there's no warning. The choice of mode depends on relative density (sands) or consistency (clays); for loose sands (Dr < 35%) and soft clays (cu < 25 kPa), use reduced bearing factors. The Vesić (1973) and Meyerhof correction factors handle this transition. For routine shallow footings on competent soil (medium-dense sand, stiff clay) general shear failure applies and the simple Terzaghi formula is appropriate.
What are the most common mistakes engineers make with bearing capacity?
The first is using ultimate capacity directly without applying a safety factor — never allowable for design. The second is ignoring settlement; in many cases settlement (typically capped at 25 mm for isolated footings, 50 mm for rafts in non-sensitive structures) governs the design before bearing capacity does, especially in cohesive soils. The third is using textbook unit weight and friction angle without site-specific testing; soil parameters can vary 30–50% across a site, and bearing capacity is sensitive to both. The fourth is forgetting the effect of groundwater; submerged soil has buoyant unit weight (≈ γ − 10 kN/m³) which reduces bearing capacity by 30–50%. The fifth is treating layered soils with a single set of parameters; if a weaker layer exists within 1–2 B below the footing, it can govern the failure mode. The sixth is using square-footing factors for strip or circular footings; shape factors apply. And the seventh is ignoring eccentric or inclined loads, which require reduced effective footing dimensions (Meyerhof's effective area method).
When should I not use this calculator?
Skip it for deep foundations (piles, drilled shafts, caissons) where the failure mechanism is fundamentally different — use pile capacity formulas based on skin friction and end bearing instead. Avoid it for footings on rock, which have their own bearing-capacity formulas (RMR or Q-system based) and are typically not limited by bearing but by serviceability or RQD-based rock-mass strength. It is the wrong tool for footings near slopes or excavations where edge effects reduce bearing capacity. Do not use it for highly compressible soils (peat, organic silts) where settlement always governs and bearing capacity is essentially irrelevant. Skip it for seismic design without applying seismic bearing-capacity factors (Richards et al.) that account for inertia effects. And for any final foundation design, get site-specific geotechnical advice and testing — a calculator estimate is fine for feasibility but inadequate for construction without verified soil parameters from a proper investigation.