How to use the Terzaghi Bearing Capacity Calculator
- 1. Enter soil propertiesCohesion c, angle φ, unit weight γ, and choose general or local shear.
- 2. Enter the footingShape, width B, depth Df and factor of safety. Add the water table if needed.
- 3. Get the capacityUltimate, net ultimate, net safe and safe bearing capacity with each term.
Terzaghi's equation and the factors used
Strip footing: qu = c·Nc + q·Nq + 0.5·γ·B·Nγ, with q = γDf. Square: 1.3cNc + qNq + 0.4γBNγ. Circular: 1.3cNc + qNq + 0.3γBNγ.
How this tool gets the factors: Nq and Nc are computed from Terzaghi's formulas, Nq = e^(2(3π/4 − φ/2)tanφ) / (2cos²(45° + φ/2)) and Nc = (Nq − 1)cotφ (5.7 for φ = 0). Terzaghi gave Nγ only as a chart, so the tool uses Kumbhojkar's (1993) values for Terzaghi's theory (as tabulated in Das), interpolated between whole degrees. You can also choose to enter the factors from your own textbook table.
For local shear (loose sand, soft clay) use c′ = ⅔c and φ′ = tan⁻¹(⅔ tanφ). Net ultimate = qu − γDf, net safe = net ultimate ÷ FS, safe = net safe + γDf.
Worked example and exam tips
Strip footing B = 2 m at Df = 1.5 m, c = 15 kN/m², φ = 30°, γ = 18 kN/m³. With book factors Nc = 37.2, Nq = 22.5, Nγ = 19.7: qu = 558 + 607.5 + 354.6 = 1520 kN/m². With the computed factors (Nγ = 19.13) the tool gives 1508 kN/m², within 1%.
- Different books round Nγ differently, so always state which table you used.
- Water table at or above the base: use γ′ = γsat − γw in the Nγ term and in q below the water table.
- Use local shear when the soil is loose or soft (low relative density, high settlement before failure).
Frequently asked questions
What is the difference between general and local shear failure?
General shear happens in dense or stiff soil with a clear failure surface and heave. Local shear happens in loose or soft soil with large settlement. Terzaghi's local shear method reduces c and tan φ to two-thirds.
Why does my book give a different Nγ?
Terzaghi gave Nγ as a chart, so books read it differently (for example 19.7 or 20.1 at 30°). The tool uses Kumbhojkar's values (19.13 at 30°) or lets you enter your book's values.
What is net safe bearing capacity?
It is the net ultimate capacity (qu − γDf) divided by the factor of safety. It is the extra pressure the soil can safely take over the soil already removed.
Is this calculator free?
Yes. You fill a short form once to see your result, and other Uncodemy tools then open without the form. Everything is calculated in your browser and nothing you type is uploaded.