What is Terzaghi's bearing capacity formula?

Terzaghi's equation is qu = c·Nc + q·Nq + 0.5·γ·B·Nγ, where c is soil cohesion, q is overburden pressure (γ·Df), γ is soil unit weight, B is footing width, and Nc, Nq, Nγ are dimensionless bearing capacity factors that depend on the friction angle φ.

How are the bearing capacity factors Nc, Nq, and Nγ calculated?

Nq = e^(π·tan φ)·tan²(45 + φ/2), Nc = (Nq − 1)·cot φ (or 5.14 for φ = 0), and Nγ = 2·(Nq + 1)·tan φ. These are the standard Terzaghi/Meyerhof expressions used in most geotechnical textbooks.

What shape factors does Terzaghi use?

Strip footing: no shape correction (factors = 1). Square footing: Nc term multiplied by 1.3, Nγ term multiplied by 0.8. Circular footing: Nc term multiplied by 1.3, Nγ term multiplied by 0.6. The Nq term is unchanged for all shapes in Terzaghi's original formulation.

What factor of safety should I use?

Most geotechnical codes recommend a factor of safety of 2.5 to 3.0 for permanent structures on shallow foundations. Use 2.0 only for temporary works or where soil parameters are well-established from thorough investigation.

Does this calculator account for water table effects?

No. The tool uses the unit weight you enter directly. If the water table is at or near the footing level, substitute the effective (buoyant) unit weight γ' = γsat − γw in the Nγ and q terms as appropriate before entering values.

Bearing Capacity (Terzaghi) Calculator

Name: Bearing Capacity (Terzaghi) Calculator
Availability: InStock
Author: Nham Vu

Enter soil cohesion, friction angle, unit weight, footing dimensions, and surcharge to instantly compute ultimate and allowable bearing capacity using Terzaghi's general equation.

Soil & Footing Parameters

Footing Shape

Cohesion c (kPa)

Use 0 for purely granular (sand) soils.

Friction angle φ (degrees)

Typical range: 25–35° for sand, 0–20° for clay.

Unit weight γ (kN/m³)

Typical: 17–20 kN/m³. Use buoyant weight below water table.

Footing width / diameter B (m)

Embedment depth Df (m)

Factor of safety FS

Typical: 2.5–3.0 for permanent structures.

Enter soil and footing parameters, then click Calculate.

Ultimate Bearing Capacity

—

q_u (kPa)

Allowable Bearing Capacity

—

q_a = q_u / FS (kPa)

Bearing Capacity Factors

N_c

—

N_q

—

N_γ

—

Calculation Breakdown

Footing shape	—
Cohesion c	—
Friction angle φ	—
Unit weight γ	—
Width / diameter B	—
Embedment depth Df	—
Overburden q = γ·Df	—
c·Nc term	—
q·Nq term	—
0.5·γ·B·Nγ term	—
qu (ultimate)	—
Factor of safety FS	—
qa (allowable)	—

Formula: q_u = s_c·c·N_c + q·N_q + s_γ·0.5·γ·B·N_γ — Terzaghi (1943). Shape factors: Strip s_c=1, s_γ=1 — Square s_c=1.3, s_γ=0.8 — Circular s_c=1.3, s_γ=0.6.

Summary

Enter soil cohesion, friction angle, unit weight, footing dimensions, and surcharge to instantly compute ultimate and allowable bearing capacity using Terzaghi's general equation.

How it works

Select the footing shape: Strip, Square, or Circular.
Enter the soil cohesion c (kPa), internal friction angle φ (degrees), and unit weight γ (kN/m³).
Enter the footing width/diameter B (m) and embedment depth Df (m).
Enter the surcharge pressure q = γ·Df if overburden soil differs, or leave the calculator to compute it automatically.
Set the desired factor of safety (commonly 2.5–3.0).
Click Calculate to see Nc, Nq, Nγ, ultimate bearing capacity qu, and allowable bearing capacity qa.

Use cases

Preliminary sizing of shallow strip and pad footings in geotechnical design.
Cross-checking hand calculations during foundation engineering coursework.
Quickly estimating safe bearing pressure before a full finite-element analysis.
Comparing bearing capacity across different friction angles and cohesion values.
Teaching Terzaghi's bearing capacity theory with an interactive step-by-step breakdown.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu