Bearing Capacity (Terzaghi) Calculator
Estimates the ultimate and allowable bearing capacity of a shallow strip footing using Terzaghi's classic bearing-capacity equation. Geotechnical and structural engineers use it for a first-pass check of soil bearing pressure before detailed design.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the soil cohesion c (kPa), friction angle φ (°) and unit weight γ (kN/m³).
- Enter the footing width B (m) and founding depth Df (m); set a factor of safety (default 3).
- Read qu (ultimate), qnet (net) and qa (allowable) — compare your applied pressure against qa.
How it works
Terzaghi's general-shear equation for a continuous (strip) footing is qu = c·Nc + q·Nq + 0.5·γ·B·Nγ, where q = γ·Df is the surcharge from the soil above founding level. The three terms represent the contributions of cohesion, surcharge and the footing's self-bearing width.
The bearing-capacity factors are computed from the friction angle φ: Nq = e^((3π/2 − φ)·tanφ)/(2·cos²(45° + φ/2)), Nc = (Nq − 1)·cotφ, and Nγ = 2·(Nq + 1)·tanφ (Vesic form). For φ = 0 (undrained clay) the factors reduce to Nc = 5.14, Nq = 1, Nγ = 0. The allowable pressure divides qu by the factor of safety.
Worked example
1.0 m deep strip footing on c–φ soil. For c = 10 kPa, φ = 30°, γ = 18 kN/m³, B = 2 m, Df = 1 m: Nq ≈ 22.46, Nc ≈ 37.16, Nγ ≈ 27.08. Surcharge q = 18 × 1 = 18 kPa. qu = 10×37.16 + 18×22.46 + 0.5×18×2×27.08 ≈ 1263 kPa; qnet ≈ 1245 kPa; with FoS 3, qa ≈ 421 kPa.
Common mistakes
- Applying the strip-footing result directly to a square or circular pad — multiply the c-term by 1.3 and the γ-term by 0.8 (square) or 1.3 and 0.6 (circular).
- Comparing the applied load against qu instead of the allowable qa (qu already includes no safety margin).
- Entering a total-stress cohesion with a drained friction angle (mixing undrained and effective-stress parameters).
Frequently asked questions
Which Nγ formula does this use?
The Vesic form Nγ = 2·(Nq + 1)·tanφ. Terzaghi's own Nγ table and other authors (Meyerhof, Hansen) give slightly different values, so factors can differ by 10–20% between references — always state the source in your report.
Is this for a strip, square or circular footing?
The equation as written is the strip (continuous) footing case. For a square footing multiply the cohesion term by 1.3 and the γ (width) term by 0.8; for a circular footing use 1.3 and 0.6.
What factor of safety should I use?
A global factor of safety of 3 on ultimate bearing capacity is the traditional value for shallow foundations. Lower values may be justified with high-quality site data and a settlement check; codes such as Eurocode 7 use partial factors instead.
How do I handle undrained clay?
Enter φ = 0 and c = the undrained shear strength cu. The tool then uses Nc = 5.14, Nq = 1, Nγ = 0, giving qu = 5.14·cu + γ·Df.
Does this include settlement?
No. Bearing capacity checks strength (failure); allowable pressure is often governed by settlement instead, which must be checked separately.
Related tools
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- Pile Capacity Calculator (end bearing + skin friction)
- Settlement (Consolidation) Calculator
- Bulk Density Calculator
- Shear Box Test Strength Parameters Calculator
- SPT N-Value to Relative Density Calculator
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