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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.

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How to use this calculator

Enter Values

Minimum 0

Range 0–50

Minimum 0

Minimum 0

Enter your values and press Calculate to see results.

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

  1. Enter the soil cohesion c (kPa), friction angle φ (°) and unit weight γ (kN/m³).
  2. Enter the footing width B (m) and founding depth Df (m); set a factor of safety (default 3).
  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.

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Cite this tool

Zerdly. (2026). Bearing Capacity (Terzaghi) Calculator. Retrieved from https://www.zerdly.com/tools/bearing-capacity-terzaghi-calculator/

Tip: Enter any known values to calculate the remaining results.

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