⛰️ Soil Bearing Capacity

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 4 independent reference calculations · how PhDino checks its numbers

The maximum pressure a shallow footing can safely put on the soil beneath it, before shear failure of the soil.

A footing fails not just when the structure above it is too weak, but also when the soil beneath it can no longer resist shear along a failure surface and the footing punches, tilts, or squeezes soil out from underneath. Terzaghi's classical bearing capacity theory computes the ultimate pressure at which this happens, combining three separate contributions: the soil's cohesion, the surcharge (weight) of soil beside the footing, and the weight of soil within the failure wedge itself.

Each contribution is scaled by a bearing capacity factor (Nc, Nq, Nγ) that depends only on the soil's friction angle — the more frictional the soil, the larger these factors and the higher the bearing capacity for the same cohesion and footing size. PhDino uses Terzaghi's equation with the Prandtl–Reissner expressions for Nq and Nc and Hansen's expression for Nγ; different authors' Nγ in particular differ by tens of percent, which is one reason results should be treated as estimates.

Key formula

q_ult = c·Nc + γ·Df·Nq + 0.5·γ·B·Nγ
Nq = e^(π·tanφ) · tan²(45° + φ/2)
Nc = (Nq − 1) / tanφ   (5.14 when φ = 0)
Nγ = 1.5 · (Nq − 1) · tanφ
q_allow = q_ult / FS  (commonly FS = 3)

Variables

c

soil cohesion

φ

soil friction angle (drives Nc, Nq, Nγ)

γ

soil unit weight

B, Df

footing width and embedment depth

How to use the Soil Bearing Capacity calculator

Use this to estimate how much pressure a shallow footing can put on the ground before the soil fails in shear, and the allowable pressure after a factor of safety of three. It is the calculation behind a footing's allowable bearing value, and it shows which soil properties, and which footing dimensions, actually earn the capacity.

The equation splits the capacity into three parts: one from the soil's cohesion, one from the weight of soil beside the footing (the surcharge), and one from the weight of the soil within the failure wedge below it. The friction angle controls how large each part can be.

Cohesion (c) (psf)

The soil's cohesion in lb/ft². Clay has a real cohesion; clean sand and gravel have effectively none. For long-term (drained) behavior of clay many designers use a much smaller cohesion than the short-term value, so take it from a geotechnical report.

Friction Angle (φ) (degrees)

The angle of internal friction in degrees: roughly 28° to 34° for loose to medium sand, 35° to 40° for dense sand, and 20° to 30° for silty and clayey soils. This is the most sensitive input, so use a conservative, measured value.

Soil Unit Weight (γ) (pcf)

The soil's unit weight in lb/ft³, typically 100 to 130 for common soils. Use the buoyant weight (about half) below the water table.

Footing Width (ft)

The footing width B in feet. For a strip footing this is the width across, not the length along the wall.

Footing Depth (ft)

The depth from the ground surface down to the bottom of the footing in feet. Only soil that will stay in place beside the footing counts; do not use depth that may later be excavated.

Worked example: a strip footing in clayey sand

A 3 ft wide strip footing for a garden wall will sit 2 ft below grade in a clayey sand with cohesion 300 lb/ft², friction angle 25° and unit weight 115 lb/ft³. What bearing capacity can be assumed?

Worked by hand:

1. Bearing capacity factors for a friction angle of 25°: N_q = e^(π tan φ) × tan²(45° + φ/2) = 10.66, N_c = (N_q − 1) ÷ tan φ = 20.72, and N_γ = 1.5 × (N_q − 1) × tan φ = 6.76.
2. Cohesion part. c × N_c = 300 × 20.72 = 6,216 lb/ft².
3. Surcharge part. γ × D_f × N_q = 115 × 2 × 10.66 = 2,452 lb/ft².
4. Soil-weight part. ½ × γ × B × N_γ = 0.5 × 115 × 3 × 6.76 = 1,166 lb/ft².
5. Ultimate capacity is the sum: 9,834 lb/ft². Allowable, with a factor of safety of 3, is 3,278 lb/ft².

About 3,278 lb/ft² (roughly 3.3 kips per ft²) is a sensible allowable pressure for this footing, before checking settlement. Notice where the capacity comes from: the soil-weight part is only about 1,166 of the 9,834 lb/ft² total, so this soil's strength is mostly its cohesion and the depth of the footing, not its width.

Reading the result: what drives capacity, and what it leaves out

The three bearing factors grow explosively with the friction angle. N_q is about 6.4 at 20°, 18.4 at 30° and 64.2 at 40°, so a small error in φ becomes a large error in capacity, and a soil that is a few degrees stronger can hold several times as much. This is the reason the friction angle should come from a test, not a table.

• Depth helps more than width in many soils. In the example, doubling the footing depth from 2 ft to 4 ft raises the capacity by about a quarter, while doubling the width from 3 ft to 6 ft raises it by about an eighth.
• Capacity is not the only limit. A footing that is safe against shear failure can still settle more than a structure tolerates, and on soft or compressible soil settlement usually decides the size.
• Water matters. A water table at or above the footing base reduces the effective weight of the soil by roughly half, and with it the surcharge and soil-weight parts.
• The equation is for a long strip footing. Square and round footings get shape factors that raise the cohesion and surcharge parts, and inclined or eccentric loads reduce capacity; none of that is included here.

Notes & limitations

• This is bearing CAPACITY (shear failure) — settlement is a separate check, and a footing sized only for bearing capacity can still settle more than a structure can tolerate. On soft or compressible soil, settlement usually governs.
• The equation assumes a long strip footing and general shear failure in dense or stiff soil; square or circular footings, loose or soft soils, inclined loads and a high water table all need correction factors that a full geotechnical analysis would include. A water table at or above the footing base cuts the effective weight of the soil to roughly half, and the surcharge and soil-weight terms of the equation drop with it.

Common mistakes

• Using a friction angle from a generic table without checking it against the actual soil. Because capacity depends so steeply on φ, an optimistic value is unsafe.
• Treating the ultimate capacity as the design pressure. The allowable value is the ultimate divided by a factor of safety, usually three.
• Counting soil that will not stay. Depth that will later be excavated for a trench or a basement stops contributing the moment it is removed.
• Ignoring groundwater. Many footings that look safe in dry conditions lose a large share of their capacity when the water table rises.
• Using short-term clay cohesion for a permanent structure. Clay softens over time, and a value appropriate for undrained loading may overstate the long-term capacity.
• Forgetting settlement, or using the bearing value for a footing on fill. Uncontrolled fill needs its own investigation and often cannot be relied on at all.

Frequently asked questions

Papers worth reading

Some recent research on the bearing capacity of foundations Meyerhof, G. G. (1963), Canadian Geotechnical Journal. Introduced the shape, depth and load-inclination factors that extend the basic bearing-capacity equation to real footings.