Foundation Bearing Capacity Calculator (Terzaghi)
Find the ultimate and allowable bearing capacity of a strip, square, or circular footing from its width, depth, and soil properties using Terzaghi's classical theory.
🏢 What is Foundation Bearing Capacity?
Foundation bearing capacity is the maximum pressure a shallow foundation can safely transfer to the soil beneath it without triggering a shear failure of that soil. Terzaghi's classical bearing capacity theory, published in 1943, remains one of the most widely taught methods for this calculation, combining three separate contributions, soil cohesion, the surcharge pressure from soil above the footing base, and the soil's own self-weight below the footing, each scaled by a bearing capacity factor (Nc, Nq, and Ngamma) that depends only on the soil's angle of internal friction.
Geotechnical engineers run this calculation at the earliest stage of foundation sizing, right after soil parameters come back from a site investigation report. A structural engineer sizing a spread footing for a column checks the allowable bearing capacity against the column's actual load before finalizing footing dimensions. A geotechnical consultant reviewing a proposed foundation layout for a new building runs the same check across several trial footing widths and depths to recommend the most economical size that still clears the required factor of safety.
A common misconception is that a single bearing capacity number applies to every footing on a site. In reality, bearing capacity depends on footing shape, width, and depth as much as it depends on the soil itself, the exact same soil supports a different allowable pressure under a strip footing than under a square or circular footing of the same width, because Terzaghi assigned different shape coefficients to the cohesion and self-weight terms for each case.
This calculator takes the footing shape, width, depth, soil cohesion, unit weight, and friction angle, and returns the ultimate bearing capacity, the allowable bearing capacity after applying your chosen factor of safety, the individual Nq, Nc, and Ngamma factors, and a chart showing how allowable bearing capacity changes as footing width changes.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Strip Footing on Cohesive-Frictional Soil
Strip footing, B = 1.5 m, Df = 1 m, c = 10 kPa, γ = 18 kN/m³, φ = 30°, FS = 3
Example 2 — Square Footing on Cohesionless Sand
Square footing, B = 2 m, Df = 1.5 m, c = 0 kPa, γ = 18 kN/m³, φ = 32°, FS = 3
Example 3 — Circular Footing on Undrained Clay (φ = 0)
Circular footing, B = 1.2 m, Df = 1 m, c = 25 kPa, γ = 17 kN/m³, φ = 0°, FS = 3
❓ Frequently Asked Questions
🔗 Related Calculators
What is Terzaghi's bearing capacity theory?
Terzaghi's bearing capacity theory is a classical method from 1943 for finding the ultimate bearing capacity of a shallow foundation, combining the soil's cohesion, the surcharge (overburden) pressure at foundation depth, and the soil's self-weight below the footing, each scaled by its own bearing capacity factor (Nc, Nq, and Ngamma) that depends only on the soil's friction angle.
How do you calculate Nq, Nc, and Ngamma?
Nq = e^(pi x tan(phi)) x tan^2(45 + phi/2), where phi is the soil friction angle. Nc = (Nq - 1) / tan(phi), with the limiting value Nc = 5.7 used at phi = 0 to avoid dividing by zero. Ngamma = (Nq - 1) x tan(1.4 x phi), Terzaghi's own widely used approximation for this factor.
What is the difference between ultimate and allowable bearing capacity?
Ultimate bearing capacity (qu) is the theoretical pressure at which the soil beneath a footing fails in shear. Allowable bearing capacity (qa) divides qu by a factor of safety, typically 2.5 to 3.5, to keep the applied pressure well below the failure point and limit settlement to an acceptable level for the structure above.
How does footing shape affect bearing capacity?
Terzaghi assigned different coefficients to the cohesion and unit-weight terms for each shape. A strip (long, continuous) footing uses 1.0 x c x Nc and 0.5 x gamma x B x Ngamma. A square footing uses 1.3 x c x Nc and 0.4 x gamma x B x Ngamma. A circular footing uses 1.3 x c x Nc and 0.3 x gamma x B x Ngamma. The surcharge term gamma x Df x Nq is identical for all three shapes.
What soil unit weight should I use if I do not have a lab test?
18 kN/m3 (this calculator's default) is a reasonable planning-stage estimate for a moist, medium-dense soil. Loose sands and soft clays can run closer to 15 to 17 kN/m3, while dense sands and gravels can exceed 20 kN/m3. A site-specific geotechnical investigation should always replace this estimate before final design.
Why does cohesion c not matter for sandy soils?
Cohesionless sands and gravels have c approximately equal to 0, since their shear strength comes entirely from internal friction between particles, not particle-to-particle bonding. For these soils, the c x Nc term drops out of the formula entirely and bearing capacity comes only from the surcharge (gamma x Df x Nq) and self-weight (gamma x B x Ngamma) terms.
What factor of safety should I use for bearing capacity?
A factor of safety of 3.0 against ultimate bearing capacity is the most common default in practice for shallow foundations under typical static loads, and is this calculator's default. Some codes and situations allow 2.5, while more conservative or poorly characterized sites may call for FS = 3.5 or higher.
Why does bearing capacity increase with footing width?
A wider footing mobilizes a larger, deeper wedge of soil beneath it in the Terzaghi failure mechanism, which increases the self-weight contribution term (the gamma x B x Ngamma component) proportionally to B. This is why the allowable bearing capacity versus width chart on this page slopes upward, though the cohesion and surcharge terms stay constant as width changes.
Is Terzaghi's theory still used today?
Yes, for preliminary design and hand-calculation checks, though many modern codes (including Eurocode 7 and various national standards) use the more general Meyerhof, Hansen, or Vesic bearing capacity equations, which add shape, depth, and inclination factors beyond Terzaghi's original three-shape approach. Terzaghi's formulas remain a widely taught and referenced starting point.
What happens to bearing capacity at phi = 0 degrees?
At phi = 0 (a purely cohesive, undrained clay condition), Nq drops to exactly 1 and Ngamma drops to exactly 0, so the formula collapses to qu = c x Nc (strip) or qu = 1.3 x c x Nc (square or circular), plus the constant surcharge term gamma x Df x 1. This calculator uses the standard limiting value Nc = 5.7 at phi = 0 rather than evaluating an undefined 0/0 division.
Does this calculator account for a water table?
No. This calculator uses the soil unit weight gamma as a single value for both the surcharge and self-weight terms, which assumes dry or moist soil conditions above and below the footing. A shallow water table reduces the effective unit weight of submerged soil and requires a separate, more detailed calculation not covered here.