Soil Bearing Capacity Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: August 19, 2026Three Separate Failure Mechanisms, Added Together
Terzaghi's 1943 bearing capacity theory treats a foundation's ultimate capacity as the sum of three independent contributions: the soil's cohesion, the surcharge pressure from soil above the footing, and the weight of soil within the failure wedge below it. Each contribution is scaled by a bearing capacity factor — Nc, Nq, and Nγ — that depends entirely on the soil's friction angle, and the shape of the footing further adjusts the cohesion and weight terms.
The Formulas
Square footing: qu = 1.3 × c × Nc + q × Nq + 0.4 × γ × B × Nγ
Circular footing: qu = 1.3 × c × Nc + q × Nq + 0.3 × γ × B × Nγ
q (surcharge) = γ × Df
Allowable Bearing Capacity = qu / Factor of Safety
Bearing Capacity Factors by Friction Angle
| Friction angle (φ) | Nc | Nq | Nγ |
|---|---|---|---|
| 0° | 5.70 | 1.00 | 0.00 |
| 20° | 17.69 | 7.44 | 0.24 |
| 25° | 25.13 | 12.72 | 0.47 |
| 30° | 37.16 | 22.46 | 0.87 |
| 35° | 57.75 | 41.44 | 1.58 |
| 40° | 95.66 | 81.27 | 2.87 |
Worked Example: Strip Footing
| Quantity | Value |
|---|---|
| Surcharge q | 18 kPa |
| Ultimate bearing capacity qu | 415.90 kPa |
| Allowable bearing capacity (qu / 3) | 138.63 kPa |
Where This Gets Used
- Sizing a shallow foundation — checking whether a proposed footing width keeps bearing pressure under the allowable capacity for the given soil.
- Comparing footing shapes — the shape correction factors on the cohesion and weight terms mean a square or circular footing behaves differently than a strip footing of the same width.
- Early geotechnical screening — a quick estimate before a full site-specific geotechnical investigation and design.
How to Use This Calculator
- Choose Unit system and Footing Shape — Strip, Square, or Circular.
- Enter Cohesion c, Soil Unit Weight, Friction Angle phi (0–45 degrees), Footing Width B, and Footing Depth Df.
- Enter Factor of Safety (defaults to 3 if left blank).
- Select Calculate to see the ultimate and allowable bearing capacity.
Related Calculations
Check the load this footing needs to carry with the Structural Load Calculator, or evaluate a nearby cut slope with the Slope Stability Calculator.
Principles of Geotechnical Soil Mechanics and Foundation Bearing Capacity
A soil bearing capacity calculator computes the ultimate and allowable soil bearing pressures supporting shallow concrete footings, slab-on-grade foundations, and retaining walls. Governed by Karl Terzaghi's Bearing Capacity Theory and modified Meyerhof formulations, geotechnical analysis prevents foundation shear failure and excessive structural differential settlement.
Terzaghi's Ultimate Bearing Capacity Equation (Strip Footing)
- c: Soil cohesion strength (psf or kPa; c = 0 for pure cohesionless sand).
- q = γ × Df: Surcharge effective overburden pressure at foundation embedment depth Df.
- γ: Moist unit weight of soil (typically 110 to 125 lbs/cu ft = 17 to 20 kN/m³).
- B: Footing foundation width (feet or meters).
- Nc, Nq, Nγ: Terzaghi Dimensionless Bearing Capacity Factors (functions of internal friction angle φ).
Allowable Bearing Capacity and Safety Factor
Standard Presumptive Soil Bearing Values (IBC Building Code)
| Soil Classification / Geological Class | Internal Friction Angle (φ) | Presumptive Allowable Bearing Capacity |
|---|---|---|
| Massive Sound Crystalline Bedrock | — | 12,000 psf (600 kPa) |
| Dense Well-Graded Gravel / Sand-Gravel | 36° to 42° | 3,000 to 4,000 psf (150 to 200 kPa) |
| Medium Stiff Sand / Sandy Gravel | 30° to 34° | 2,000 psf (100 kPa) |
| Stiff Inorganic Silt / Cohesive Clay | Cohesion c > 1,000 psf | 1,500 psf (75 kPa) |
| Soft Clay / Organic Peat | — | < 500 psf (Requires deep pile foundations) |
Step-by-Step Worked Calculation Example
Example: Sizing a Square Footing in Dense Sand (φ = 30°)
Problem: A building column carries a dead + live load of 120,000 lbs (120 kips). The footing is embedded Df = 3.0 feet deep in sandy soil with unit weight γ = 120 pcf and friction angle φ = 30° (c = 0; Nq = 18.4, Nγ = 22.4). Using a 3.0 factor of safety, calculate: (1) Ultimate bearing capacity for a 5-ft square footing; (2) Allowable bearing pressure; and (3) Footing safety compliance.
Step 1: Calculate Surcharge Overburden Pressure (q = γ × Df):
q = 120 pcf × 3.0 ft = 360.0 psf
Step 2: Calculate Ultimate Bearing Capacity (qult for square footing = 1.2·c·Nc + q·Nq + 0.4·γ·B·Nγ):
qult = 0 + ( 360 × 18.4 ) + ( 0.4 × 120 × 5.0 × 22.4 )
qult = 6,624 + 5,376 = 12,000.0 psf
Step 3: Calculate Allowable Bearing Capacity (FS = 3.0):
qallow = 12,000.0 / 3.0 = 4,000.0 psf (4.0 ksf)
Step 4: Verify Column Bearing Stress on 5ft × 5ft Footing (Area = 25 sq ft):
Actual Soil Stress = 120,000 lbs / 25 sq ft = 4,800 psf (> 4,000 psf — slightly undersized!)
Increase footing size to 5.5 ft × 5.5 ft (Area = 30.25 sq ft &implies; Stress = 3,967 psf ≤ 4,000 psf).
Conclusion: A 5.5ft × 5.5ft reinforced concrete footing safely supports the column load.
Groundwater Table Elevation Impact on Soil Strength
In geotechnical engineering, the presence of a high groundwater table drastically reduces soil bearing capacity. When soil pores become fully submerged below the water table, buoyant pore water pressure counteracts grain-to-grain contact stresses:
Because submerged unit weight γ' is roughly half of moist soil weight, a rising seasonal water table intersecting the footing foundation base slashes soil bearing capacity by up to 50%.
Immediate Elastic vs. Long-Term Consolidation Settlement
- Immediate Elastic Settlement (δe): Occurs instantaneously in granular sands and gravels as soil grains rearrange under load.
- Primary Consolidation Settlement (δc): Occurs gradually over months or decades in saturated clay strata as water is slowly squeezed out of microscopic clay pores (governed by Terzaghi's 1D Consolidation Theory).
Footing Eccentricity and Overturning Moment Checks
When structural columns transfer lateral wind or earthquake seismic shear loads to shallow footings, the applied load becomes eccentric (e = M / P).
To prevent foundation base separation and edge uplift, the eccentricity must remain within the Middle Third Kern (e ≤ B / 6), guaranteeing uniform compressive soil contact pressure across the entire footing footprint.
Standard Penetration Test (SPT N-Value) Correlations
Geotechnical field boring logs record the SPT N-Value (hammer blow counts per foot of penetration), correlating directly with internal friction angles (φ = 28° + 0.3×N) and allowable foundation bearing pressures.
Mat and Raft Foundation Load Distribution
On highly compressible or variable alluvial soils, structural engineers design thick continuous reinforced concrete Mat Foundations that distribute heavy superstructure building column loads across the entire building footprint.