What is Terzaghi's bearing capacity equation?

Terzaghi's general bearing capacity equation expresses the ultimate bearing capacity as q_ult = c·Nc·sc + q·Nq + 0.5·γ·B·Nγ·sγ, where Nc, Nq, and Nγ are dimensionless bearing capacity factors that depend on the soil friction angle φ, and sc, sγ are shape correction factors.

What is the difference between ultimate and allowable bearing capacity?

Ultimate bearing capacity (q_ult) is the theoretical maximum load per unit area the soil can sustain before shear failure. Allowable bearing capacity (q_all) divides q_ult by a factor of safety (typically 2.5–3) to account for uncertainty and prevent excessive settlement.

What factor of safety should I use?

A factor of safety of 3.0 is common for permanent structures with uncertain soil data. A value of 2.5 may be used when soil parameters are well-established from detailed site investigation. For temporary structures, 2.0 is sometimes acceptable.

Does this account for settlement?

No. This calculator addresses shear failure only. Allowable bearing capacity based on settlement limits is often more restrictive than the shear-failure value, especially for loose sands or soft clays. A full settlement analysis should accompany any foundation design.

What are the bearing capacity factors Nc, Nq, and Nγ?

They are derived from Terzaghi's theory: Nq = e^(π·tan φ)·tan²(45+φ/2), Nc = (Nq−1)·cot φ (or 5.14 when φ=0), and Nγ = 2·(Nq+1)·tan φ. All three increase significantly as the friction angle rises.

Is this suitable for deep foundations?

No. Terzaghi's equation applies to shallow foundations where the depth-to-width ratio (Df/B) is approximately ≤1. For deep foundations such as piles or caissons, different analytical methods are required.

Soil Bearing Capacity Calculator

Name: Soil Bearing Capacity Calculator
Availability: InStock
Author: Nham Vu

Calculate ultimate and allowable soil bearing capacity for strip, square, or circular shallow foundations using Terzaghi's equation.

Foundation & Soil Parameters

Foundation Shape

Soil Properties

Cohesion, c (kPa)

0 for purely frictional sand; >0 for clay or mixed soils

Friction Angle, φ (degrees)

Typical range: 0° (soft clay) to 40° (dense gravel)

Unit Weight, γ (kN/m³)

Typical: 17–21 kN/m³ for most soils

Foundation Geometry

Width / Diameter, B (m)

Founding Depth, D_f (m)

Factor of Safety, FS

Typically 2.5–3.0 for buildings

Enter soil parameters and click Calculate

Summary

Calculate ultimate and allowable soil bearing capacity for strip, square, or circular shallow foundations using Terzaghi's equation.

How it works

Select the foundation shape: strip, square, or circular.
Enter soil properties: cohesion (c), unit weight (γ), and friction angle (φ).
Enter foundation geometry: width (B) and depth (Df).
Choose a factor of safety (typically 2.5–3.0 for buildings).
The calculator applies Terzaghi's bearing capacity equation to compute q_ult.
Allowable bearing capacity equals q_ult divided by the factor of safety.

Use cases

Preliminary sizing of spread footings and mat foundations.
Geotechnical checks during early structural design.
Educational exercises on Terzaghi's bearing capacity theory.
Comparing bearing capacity for different foundation widths and depths.
Estimating safe load limits for strip footings on cohesive clay.
Verifying soil suitability before detailed foundation design.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu