Terzaghi Bearing Capacity Calculator for Shallow Foundations

Terzaghi’s bearing capacity equation, published in 1943, remains the starting point for shallow foundation design. It estimates the ultimate pressure a footing can carry before the soil beneath it fails in general shear, based on the soil’s cohesion and friction angle, the footing’s depth and width, and the unit weight of the surrounding soil. This calculator applies the full equation with shape factors and a water table correction.

The bearing capacity equation

For a strip (continuous) footing:

q_ult = c x Nc + q x Nq + 0.5 x gamma x B x N-gamma

Square and circular footings use shape factors on the first and third terms: 1.3 x c x Nc + q x Nq + 0.4 x gamma x B x N-gamma for square footings, and 1.3 x c x Nc + q x Nq + 0.3 x gamma x B x N-gamma for circular footings. Here q is the effective overburden pressure at the footing base, and B is the footing width or diameter.

Bearing capacity factors

Terzaghi expressed Nq and Nc in closed form:

• Nq = e^((3 pi/2 minus phi) tan phi) / (2 cos squared(45 + phi/2))
• Nc = (Nq minus 1) x cot(phi), or 5.7 when phi = 0
• N-gamma has no closed form in Terzaghi’s original work and came from a graphical solution. This calculator uses the widely cited approximation N-gamma = (Nq minus 1) x tan(1.4 phi), which tracks Terzaghi’s tabulated values closely across the typical design range

Water table effects

A shallow water table reduces bearing capacity because buoyancy lowers the effective unit weight of the soil. This calculator applies the standard correction: if the water table sits at or above the footing base, the surcharge term uses effective (submerged) unit weight below the water table, and the unit weight term uses the fully submerged value. If the water table falls within the failure zone below the footing (between the base and one footing width deeper), the calculator linearly interpolates between submerged and moist unit weight.

Worked example

Consider a 2 m wide strip footing at 1.5 m depth in a cohesionless sand (c = 0, phi = 30 degrees, gamma = 18 kN/m3), with the water table far below at 10 m, and a factor of safety of 3.

1. Nq = 22.46, Nc = 37.16, N-gamma = 19.32
2. Overburden, q = 18 x 1.5 = 27 kPa
3. Surcharge term = 27 x 22.46 = 606.3 kPa
4. Unit weight term = 0.5 x 18 x 2 x 19.32 = 347.7 kPa
5. q_ult = 0 + 606.3 + 347.7 = 954 kPa
6. q_allow = 954 / 3 = 318 kPa

These are the exact numbers the calculator returns when you click Load Example, confirming the tool matches a hand calculation before applying it to real design parameters.

Limitations

Terzaghi’s equation assumes general shear failure, a rough footing base, and a homogeneous soil, and it does not include depth, inclination, or eccentricity factors used in more modern methods like Meyerhof or Hansen. It remains widely used for preliminary design and as a check against more detailed analyses, but final foundation design should follow the applicable local building code and a full geotechnical investigation.

Worth remembering: Terzaghi’s bearing capacity factors assume a general shear failure, which tends to overestimate capacity for loose sands or soft clays that actually fail in local or punching shear. If your borings show loose, compressible, or very soft material, it is common practice to reduce the friction angle and cohesion inputs before running the numbers, rather than trusting the raw lab values at face value. That adjustment alone can change a bearing capacity result more than any other single input in the equation.

Related Calculator and Reference

See also the Bearing Pressure Converter for moving that ultimate capacity between kPa, tsf, ksf and kg per square centimetre, with the short and long ton kept apart.

For deep foundation capacity using similar soil strength parameters, see the Pile Bearing Capacity Estimator. For background on Terzaghi’s bearing capacity theory, see the FHWA reference on shallow foundation bearing capacity.