Soil Bearing Capacity Calculator
Calculate ultimate and allowable soil bearing capacity using Terzaghi's equation. Inputs include soil cohesion, friction angle, and foundation geometry.
About this calculator
This calculator applies Terzaghi's classic bearing capacity equation, qu = cNc + qNq + 0.5γBNγ, to find how much pressure a shallow strip or square footing can safely carry. The three bearing capacity factors — Nc, Nq, and Nγ — are computed directly from the soil's internal friction angle using the standard closed-form relationships (Nq from the friction angle through an exponential/tangent expression, Nc from Nq for frictional soils or a fixed 5.14 for purely cohesive soil, and Nγ from Nq), so changing the friction angle shifts all three simultaneously. The three additive terms represent cohesion's contribution, the surcharge from soil above the footing base, and the footing's own width interacting with the soil's self-weight — meaning capacity increases with both embedment depth and footing width, not just soil strength.
Ultimate bearing capacity is divided by a factor of safety of 3 (standard practice for allowable stress design) to give the allowable bearing pressure, and a separate "net allowable" figure subtracts the overburden pressure already present before construction, which matters because that overburden doesn't represent additional load your foundation adds to the soil. The model assumes a single homogeneous soil layer, no water table effects, and general shear failure — real sites often have layered soils, groundwater, or local shear/punching failure modes that this simplified check doesn't capture, so treat the result as a preliminary estimate to compare against a geotechnical report.
Inputs
Soft clay: 200–500 psf; stiff clay: 1,000–2,000 psf; hard clay: 2,000–4,000 psf
ASTM D3080: loose sand 28–32°; dense sand 36–40°; gravel 40–45°; clay 0–15°
Results
Ultimate Bearing Capacity
18,029 psf
Allowable Bearing (FS=3)
6,010 psf
How to Use This Calculator
- Enter soil cohesion (psf), friction angle (°), foundation width (B), foundation depth (D), and soil unit weight.
- Review Ultimate Bearing Capacity and Allowable Bearing Capacity (FS=3) in psf.
- Compare allowable bearing to your design footing pressure — reduce footing load or increase width if needed.
How the result changes with Friction Angle (φ)
| Friction Angle (φ) | Ultimate Bearing Capacity | Allowable Bearing (FS=3) |
|---|---|---|
| 15 | 4,250 psf | 1,417 psf |
| 23 | 8,696 psf | 2,899 psf |
| 45 | 140,549 psf | 46,850 psf |
| 50 | 351,323 psf | 117,108 psf |
What each input means
- Soil Cohesion (c)
- Undrained shear strength of cohesive soil per ASCE 7 §12.13 and geotechnical reports. Sand/gravel ≈ 0 (frictional only); soft clay ≈ 200-500 psf; stiff clay ≈ 1,000-2,000 psf; hard clay ≈ 2,000-4,000 psf.
- Friction Angle (φ)
- Internal friction angle from soil testing (ASTM D3080 or SPT correlation). Loose sand ≈ 28–32°; medium sand ≈ 32–36°; dense sand ≈ 36–40°; clay ≈ 0–15°. Per ASCE 7 and geotechnical practice.
- Foundation Width (B)
- Width of the strip or square footing. Wider foundations have higher total capacity but lower unit pressure.
- Foundation Depth (D)
- Depth of the foundation below ground surface. Deeper embedment increases bearing capacity via overburden.
- Soil Unit Weight (γ)
- Unit weight of soil. Loose sand ≈ 100 pcf; dense sand ≈ 130 pcf; clay ≈ 110-125 pcf.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersSoil Cohesion (c) = 200, Friction Angle (φ) = 30, Foundation Width (B) = 4, Foundation Depth (D) = 3 = 5 input(s) provided
- Calculate Ultimate Bearing CapacityUltimate Bearing Capacity18029 = 18029
- Calculate Allowable BearingAllowable Bearing6010 = 6010
- Calculate Net Allowable BearingNet Allowable Bearing5890 = 5890
- Calculate Bearing Factor NcBearing Factor Nc30.14 = 30.14
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why do Nc, Nq, and Nγ all change when I adjust the friction angle?
All three bearing capacity factors are derived from the same friction angle: Nq comes directly from an exponential/tangent expression of phi, Nc is computed from Nq (or fixed at 5.14 when friction angle is zero), and Nγ is computed from Nq as well. Because they share that one input, increasing the friction angle raises all three factors together rather than affecting just one term of the bearing capacity equation.
What's the difference between 'Allowable Bearing' and 'Net Allowable Bearing'?
Allowable Bearing is simply the ultimate bearing capacity divided by the factor of safety of 3. Net Allowable Bearing subtracts the overburden pressure (soil unit weight times foundation depth) from the ultimate capacity before dividing by 3, because that overburden pressure already exists in the ground before the foundation is built and isn't additional load the footing adds — so it's the more relevant number for sizing a footing against its actual applied load.
Does increasing foundation depth or foundation width have the same effect on capacity?
No. Foundation depth raises capacity through the surcharge term (q × Nq, where q = soil unit weight × depth), while foundation width raises capacity through the self-weight term (0.5 × γ × B × Nγ). Both increase ultimate bearing capacity, but they do it through different terms in the equation, and depth also increases the overburden that gets subtracted out in the net allowable figure.
Why is the ultimate bearing capacity divided by a factor of safety of 3?
A factor of safety of 3 is standard practice for allowable-stress-design foundation sizing, accounting for uncertainty in soil parameters and possible progressive or local failure modes not captured by the general shear-failure assumption in Terzaghi's equation. This calculator applies that fixed factor rather than letting it vary with soil investigation quality or project risk tolerance.
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