General bearing eq.Vesic factorsFree

Bearing
Capacity

Ultimate and allowable bearing capacity of a shallow footing from the general bearing-capacity equation, with Vesic bearing factors and footing-shape factors.

Who it's for: Geotechnical and structural engineers sizing shallow footings at the preliminary stage. You need cohesion, friction angle, and unit weight from a site investigation, plus the footing dimensions and founding depth — this is a code-method tool, not a rough estimate.

qu = c·Nc·sc + q·Nq·sq + 0.5·γ·B·Nγ·sγ

Nq = e^(π·tanφ)·tan²(45+φ/2); Nc = (Nq−1)·cotφ (φ=0 → 5.14); Nγ = 2(Nq+1)·tanφ (Vesic). q = γ·Df. Allowable qa = qu / FoS (typ. 2.5–3.0). Drained (c′,φ′) or undrained (cu, φ=0) as appropriate.

Bearing

qu · qa

How to use this calculator

Enter cohesion c

Use undrained shear strength c_u for saturated clays under rapid loading (set φ = 0), or the effective cohesion c′ for a drained analysis. Enter 0 for clean sand.

Enter friction angle φ

The internal friction angle of the bearing stratum: 0° for undrained clay, or the drained φ′ from triaxial/direct-shear tests or an SPT correlation (typically 28–38° for sand).

Enter unit weight γ and founding depth Df

γ is the in-situ unit weight of the bearing soil (17–21 kN/m³ for most soils; 18 kN/m³ is a common starting point). Df is the depth from finished ground surface to the base of the footing.

Enter footing width B and pick footing shape

B is the shorter plan dimension in metres (or the diameter for a circular footing). Shape factors for square and circular footings increase ultimate capacity over the equivalent strip.

Set the factor of safety

FoS 2.5–3.0 is conventional for permanent structural loads. Use 3.0 where site investigation is limited; 2.5 may be accepted when a detailed investigation and settlement check are complete.

Read allowable bearing qa

The result panel shows the three contributing terms, the ultimate qu, and the allowable q_a = q_u ÷ FoS for preliminary footing sizing.

The formula

Ultimate bearing capacity sums three soil mechanisms — cohesion, overburden surcharge, and soil wedge self-weight — each amplified by a Vesic bearing factor and a shape correction.

q_u = c·N_c·s_c + q·N_q·s_q + 0.5·γ·B·N_γ·s_γ

c = cohesion (kPa)
q = γ·D_f = surcharge at founding level (kPa)
γ = soil unit weight (kN/m³)
B = footing width (m)
N_c, N_q, N_γ = Vesic bearing factors (functions of φ): N_q = e^π·tanφ·tan²(45+φ/2); N_c = (N_q−1)·cotφ (→ 5.14 at φ = 0); N_γ = 2(N_q+1)·tanφ
s_c, s_q, s_γ = shape correction factors (all 1.0 for strip; square/circular increase s_c and s_q)
Allowable: q_a = q_u ÷ FoS

Worked example

Example

A 2 m × 2 m square footing at D_f = 1 m depth in soil with c = 10 kPa, φ = 30°, γ = 18 kN/m³. Vesic factors: N_c = 30.14, N_q = 18.40, N_γ = 22.40. Shape corrections (square): s_c = 1.61, s_q = 1.58, s_γ = 0.60. Surcharge q = 18 × 1 = 18 kPa. Ultimate: 10×30.14×1.61 + 18×18.40×1.58 + 0.5×18×2×22.40×0.60 = 485 + 522 + 242 = 1,250 kPa. Allowable at FoS 3: q_a = 417 kPa.

When this estimate will be off

Assumes a vertical, centrally loaded footing on level ground — inclined loads, eccentric loading, or sloping ground all reduce capacity and require separate correction factors not included here.
No water-table correction: if the water table is within B of the base, the effective unit weight of the failing wedge drops toward γ − γw, reducing the third term substantially.
No depth correction factors (dc, dq, dγ) are applied — results are conservative for footings whose Df/B ratio is greater than about 0.5.
Capacity alone does not govern serviceability: allowable bearing from this tool may still permit settlements that control the design. Always run a separate settlement estimate.

Frequently asked questions

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

They quantify the contribution of each failure mechanism. At φ = 30°: N_q ≈ 18.4, N_c ≈ 30.1, N_γ ≈ 22.4. All three grow rapidly with φ — a 5° increase in friction angle can roughly double N_q — making φ the most sensitive input.

What factor of safety should I use for bearing capacity?

Conventional practice is FoS 2.5–3.0 for permanent structural loads. Use 3.0 when site investigation is limited or soil conditions are variable; 2.5 may be acceptable when a detailed investigation and settlement check confirm adequate margin. Never reduce FoS without a licensed geotechnical engineer's judgment.

When should I use undrained versus drained parameters?

For saturated cohesive soils under rapid (undrained) loading, use c_u with φ = 0. For granular soils or long-term loading of clays, use effective-stress parameters c′ and φ′. Mixing drained and undrained parameters in the same analysis gives physically meaningless results.

Does this match the Eurocode 7 bearing resistance formula?

The bearing factor expressions (Nq, Nc, Nγ) used here match EN 1997-1 Annex D. However, the calculator applies a global factor of safety on qu rather than EC7 partial factors on actions and material properties. Convert to the GEO limit-state format for a code-compliant design submission.

Sources

Vesic (1973) — bearing-capacity factors Nc, Nq, Nγ and shape correction factors for strip, square, and circular footings
EN 1997-1 (Eurocode 7), Annex D — analytical method for bearing resistance of spread foundations using equivalent Nq, Nc, Nγ expressions

This free Calculator is built and maintained by DataDrivenAEC, using the relevant codes and standards. It does not substitute for professional judgment.