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Soil Bearing Capacity Calculator (Terzaghi)

Karl Terzaghi formulated the classic shallow foundation bearing capacity theory in 1943, modeling general shear failure across elastic, radial, and passive shear zones.

Shape of concrete foundation footing.

Foundation footing width B in meters.

Depth of foundation base below finished ground level.

Bulk density unit weight of bearing soil stratum.

Soil undrained cohesion in kPa (0 for pure sand/gravel).

Soil angle of internal friction in degrees.

Safety margin factor against shear failure (industry standard = 3.0).

Calculated Result
1006.2 kPa

Allowable Bearing Capacity (q_all)

Allowable Bearing Capacity (q_all)

1006.2 kPa (FS = 3)

Ultimate Bearing Capacity (q_ult)

3018.6 kPa

Overburden Pressure (q = γ·Df)

27.8 kPa

Bearing Capacity Factors

Nc = 31.61, Nq = 17.81, Nγ = 128.92

Footing Footprint

SQUARE (B = 2 m, Df = 1.5 m)

Calculation Breakdown

  1. 1. Terzaghi Factors EvaluationFor internal friction φ = 28°: Nc = 31.61, Nq = 17.81, Nγ = 128.92
  2. 2. Ultimate Bearing Capacity Equationq_ult = s_c·c·Nc + γ·Df·Nq + s_γ·γ·B·Nγ = (1.3 · 15 · 31.61) + (27.8 · 17.81) + (0.4 · 18.5 · 2 · 128.92) = 3018.6 kPa
  3. 3. Allowable Foundation Pressureq_all = q_ult / FS = 3018.6 / 3 = 1006.2 kPa

Bearing Capacity Contributions (kPa)

Interactive visualization based on your current inputs

Stress (kPa)
0.02655317961.1kCohesion TermOverburden SurchargeSoil Self-Weight WidthTotal Ultimate (q_ult)Allowable (FS = 3.0)ComponentStress (kPa)

What Is the Soil Bearing Capacity Calculator (Terzaghi)?

Soil bearing capacity is the maximum average contact pressure between a foundation footing and subgrade soil before shear rupture occurs.

How Does the Soil Bearing Capacity Calculator (Terzaghi) Work?

Calculates plastic limit equilibrium assuming Prandtl-Reissner log-spiral failure slip surfaces extending upward from footing edges.

Soil Bearing Capacity Calculator (Terzaghi) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

q_{ult} = s_c c N_c + \gamma D_f N_q + s_\gamma \gamma B N_\gamma, \quad q_{all} = \frac{q_{ult}}{\text{FS}}

Ultimate bearing capacity sums cohesion resistance, embedment overburden surcharge, and footing base width self-weight resistance.

How to Use the Soil Bearing Capacity Calculator (Terzaghi)

  1. Select square, strip, or circular footing geometry.
  2. Enter footing width B and embedment depth Df in meters.
  3. Input soil unit weight, cohesion c, and friction angle φ.
  4. Specify design Factor of Safety.

Step-by-Step Example Calculation

2m Square Footing in Silty Sand (c = 15 kPa, φ = 28°, Df = 1.5m)

Input Values:

footingType:square
footingWidthMeters:2.0
embedmentDepthMeters:1.5
soilUnitWeightKNm3:18.5
cohesionKPa:15.0
frictionAngleDeg:28.0
factorOfSafety:3.0
Worked Steps: Ultimate bearing capacity is 1,061.3 kPa. With FS = 3.0, allowable soil bearing pressure is 353.8 kPa (7,390 psf).

Understanding Your Result

Allowable Bearing Capacity (q_all): Safe working pressure limit for structural column load sizing.

Ultimate Capacity (q_ult): Theoretical catastrophic shear failure threshold.

Terzaghi Factors: Dimensionless Nc, Nq, and Nγ capacity factors.

Factors That Affect the Result

  • Friction angle φ has exponential impact on bearing capacity factors; footing width B linearly scales self-weight term.

When Should You Use This Calculator?

  • Structural column pad footing design, foundation engineering reports, and geotechnical site assessment.

Assumptions & Limitations

  • Valid for shallow foundations (Df ≤ B) in homogeneous soil with general shear failure mode.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard classical Terzaghi shallow foundation formulation.

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