Bearing Capacity Calculator (Terzaghi & Meyerhof)

Compute ultimate and allowable soil bearing capacity for shallow foundations using Terzaghi or Meyerhof methods, including shape, depth, and load factors.

Geotechnical Shallow foundations Strip / square / circular

Bearing Capacity Calculator

Soil parameters
Footing geometry & depth

For strip footing, use long dimension; for square/circular, set L ≈ B.

Groundwater & safety

Assumes water table at or below footing base.

Depth below ground surface (same unit as B).

Optional: Check applied load
If you enter Q, the tool will compare it with the allowable capacity and show a utilization ratio.

What is soil bearing capacity?

Soil bearing capacity is the maximum contact pressure that the ground can safely carry under a foundation without shear failure or excessive settlement. For shallow foundations (footings), we usually distinguish between:

  • Ultimate bearing capacity \(q_\text{ult}\): the theoretical pressure at which the soil fails in shear.
  • Allowable bearing capacity \(q_\text{allow}\): the design pressure, obtained by dividing \(q_\text{ult}\) by a factor of safety.

Equations used in this calculator

This tool implements classical bearing capacity equations for shallow foundations on homogeneous soil.

1. Terzaghi bearing capacity equation (strip footing)

For a strip footing at depth \(D_f\) with width \(B\):

\[ q_\text{ult} = c N_c + \gamma D_f N_q + 0.5 \gamma B N_\gamma \]

where:

  • \(c\) = soil cohesion
  • \(\gamma\) = unit weight of soil
  • \(D_f\) = footing depth below ground surface
  • \(B\) = footing width
  • \(N_c, N_q, N_\gamma\) = bearing capacity factors (functions of friction angle \(\phi\))

2. Meyerhof bearing capacity equation (with factors)

For general footing shapes and depths, Meyerhof introduced shape, depth, and load inclination factors:

\[ q_\text{ult} = c N_c s_c d_c i_c + \gamma D_f N_q s_q d_q i_q + 0.5 \gamma B N_\gamma s_\gamma d_\gamma i_\gamma \]

where \(s\), \(d\), and \(i\) are shape, depth, and load factors respectively. This calculator uses typical values for vertical centric loading.

3. Bearing capacity factors

The bearing capacity factors are computed from the friction angle \(\phi\) (in radians):

\[ N_q = e^{\pi \tan\phi} \tan^2\left(45^\circ + \frac{\phi}{2}\right) \] \[ N_c = \frac{N_q - 1}{\tan\phi} \] \[ N_\gamma = 2 (N_q + 1) \tan\phi \]

4. Allowable bearing capacity

Once the ultimate capacity is known, the allowable capacity is:

\[ q_\text{allow} = \frac{q_\text{ult}}{\text{FS}} \]

where FS is the factor of safety (commonly 2.5–3.0 for shallow foundations in many codes).

Shape and depth factors used

For Meyerhof’s method and vertical centric loading, this calculator uses commonly adopted approximations:

  • Strip footing: \(s_c = 1.0\), \(s_q = 1.0\), \(s_\gamma = 1.0\)
  • Square footing: \(s_c \approx 1 + 0.2 \frac{B}{L}\), \(s_q \approx 1 + 0.1 \frac{B}{L}\), \(s_\gamma \approx 1 - 0.4 \frac{B}{L}\)
  • Circular footing: \(s_c \approx 1.3\), \(s_q \approx 1.2\), \(s_\gamma \approx 0.6\)

Depth factors are approximated as:

  • \(d_c \approx 1 + 0.2 \frac{D_f}{B}\)
  • \(d_q \approx 1 + 0.1 \frac{D_f}{B}\)
  • \(d_\gamma \approx 1.0\)

Load inclination factors are taken as 1.0 for vertical centric loads.

Groundwater correction

When the groundwater table is close to the footing base, the effective unit weight of the soil is reduced. This calculator applies a simple correction:

  • If water table is deeper than the footing base, no correction is applied.
  • If water table is at or above the base, the submerged unit weight \(\gamma' = \gamma - \gamma_w\) is used below the water table.

For rigorous design, consult your geotechnical report, which should already account for groundwater conditions.

Typical allowable bearing capacities by soil type

The table below shows very approximate values often used for early feasibility checks (do not use for final design):

Soil type qallow (kPa) qallow (ksf)
Soft clay 50–100 1–2
Medium dense sand 150–250 3–5
Dense sand / gravel 250–400 5–8
Stiff clay 150–300 3–6

Limitations and good practice

  • This calculator assumes shallow foundations on homogeneous soil with vertical centric loading.
  • It does not explicitly check settlements; allowable capacity may be governed by settlement rather than shear.
  • Layered soils, sloping ground, eccentric or inclined loads, and seismic conditions require more advanced analysis.
  • Always base final design on a site-specific geotechnical investigation and applicable design codes (e.g., Eurocode 7, ACI/ASCE, local standards).

Bearing capacity – frequently asked questions

What is a reasonable factor of safety for bearing capacity?

For shallow foundations, factors of safety between 2.5 and 3.0 are common in many codes when using classical bearing capacity equations. Lower or higher values may be justified depending on soil variability, consequence of failure, and whether settlements are explicitly checked.

Can I use this calculator for deep foundations (piles)?

No. Pile and drilled shaft capacities are governed by different mechanisms (shaft friction and end bearing) and require dedicated methods. This tool is only for shallow foundations such as isolated, strip, or mat footings.

How accurate are the bearing capacity factors Nc, Nq, Nγ?

The factors are computed from standard closed-form expressions based on the friction angle φ. For routine design they are sufficiently accurate, but in critical projects engineers may use code-specific charts or numerical analysis.