Free Soil Bearing Capacity Calculator Using Terzaghi’s Formula

Soil bearing capacity is the maximum load per unit area that soil can support without experiencing shear failure or excessive settlement. It governs the size of every footing, column pad, and wall foundation in a building or structure. If the actual load from the building exceeds the allowable bearing capacity, the footing either punches through the soil or causes the soil to heave sideways, both of which result in catastrophic structural failure. In US construction, bearing capacity is calculated using methods established by ASTM D1143, ASCE 7, and IBC Chapter 18, and the results must be confirmed by a licensed geotechnical engineer for any permitted structure.

The FOS of 3.0 accounts for three main sources of uncertainty that are unavoidable in routine geotechnical practice: (1) spatial variability in soil properties that even thorough boring programs cannot fully capture, (2) the difference between small laboratory samples and the actual failure volume of soil beneath a loaded footing, and (3) long-term changes in soil strength due to wetting, drying, seasonal fluctuations, and adjacent construction. The ASCE standard recommends FOS 3.0 for permanent structures under static load, FOS 2.0 for wind or seismic load combinations, and FOS 1.5 for temporary construction loads. Using a higher FOS than required adds cost without meaningfully improving safety; using a lower FOS than required increases risk without reducing cost.

Terzaghi observed through experiments that the geometry of a footing affects how the soil failure wedge develops beneath it. A strip footing (also called a continuous wall footing) mobilizes a plane-strain failure mechanism, which gives it the lowest shape correction factors but is the most conservative base case. Square and circular footings develop a three-dimensional failure mechanism that provides more soil resistance, which is why the cohesion term gets multiplied by 1.3 for these shapes. Circular footings also get a smaller self-weight multiplier (0.3) compared to square (0.4) because the curved boundary reduces the effective failure volume on the sides. For rectangular footings, Terzaghi’s equations interpolate between strip and square behavior using the B/L ratio.

Groundwater reduces bearing capacity by decreasing the effective unit weight of soil. Submerged soil weighs approximately 62.4 pcf less per cubic foot than dry soil because the water buoys the soil particles upward. This effect reduces both the surcharge term (q = effective gamma times depth) and the self-weight term (gamma in the Ngamma term). For a sandy site with gamma = 120 pcf and seasonal high groundwater at the footing base, the effective gamma for the self-weight term drops to about 57.6 pcf (120 minus 62.4), cutting the Ngamma contribution by more than half. This is the single most common calculation error on US job sites where groundwater tables fluctuate seasonally, and it is exactly why our tool implements the full three-case groundwater correction table from FHWA NHI-06-089.

Terzaghi recommended using local shear failure mode when the soil is too loose or too soft to develop a complete Prandtl-type failure surface. In practice, this occurs when the friction angle phi is below approximately 28 degrees. For these conditions, Terzaghi reduced the effective cohesion to two-thirds of the measured value and replaced phi with the arctangent of two-thirds times tan(phi). Our Auto-Detect mode applies this reduction automatically when phi falls below 28 degrees. You can also force local shear mode manually, which is appropriate for preliminary conservative estimates on sites where exact soil parameters are not yet confirmed by laboratory testing.

For granular soils (sands and gravels), the Meyerhof correlation is a widely used starting point: phi approximately equals 25 plus 0.15 times the corrected N60 value, capped at 45 degrees. So N = 20 gives phi approximately 28 deg, and N = 40 gives phi approximately 31 deg. For cohesive soils (clays and silts), the undrained cohesion Su approximately equals 29 times N60 to the power 0.72 for normally consolidated clays, or use the consistency classification: N = 4 to 8 (soft, Su 250 to 500 psf), N = 8 to 15 (medium, Su 500 to 1,000 psf), N = 15 to 30 (stiff, Su 1,000 to 2,000 psf), N above 30 (hard, Su over 2,000 psf). These correlations carry significant uncertainty. Confirm with at least one direct shear test or unconfined compression test before finalizing foundation design.

Terzaghi’s 1943 equations remain the standard for routine shallow foundation design throughout the US. More advanced formulas by Meyerhof (1963), Hansen (1970), and Vesic (1973) add shape, depth, inclination, and base tilt correction factors that Terzaghi’s original equations omit, and they are used on more complex projects. However, Terzaghi’s equations are still accepted by most US building departments for standard soil conditions, and they are conservative, which is a safety advantage. ASCE 7, IBC Chapter 18, and FHWA NHI manuals all reference Terzaghi’s framework as the foundational method. For inclined loads, eccentric loading, or sloped ground surfaces, move to Hansen or Vesic formulations with more complete correction factor sets.

IBC 2021 Table 1806.2 provides presumptive allowable bearing pressures that building departments can accept without a geotechnical investigation for simple, low-risk structures. Values range from 1,500 psf for sandy clay or silty clay, to 2,000 psf for sand and silty sand, to 3,000 psf for sandy gravel or gravel, up to 12,000 psf for crystalline bedrock. These presumptive values are conservative by design. Most real soil conditions, once tested, will support higher allowable pressures than the IBC presumptive values, which is why a geotechnical investigation typically pays for itself in foundation cost savings on any building over 5,000 square feet of floor area.

Eccentric loading occurs when the resultant column load does not act through the centroid of the footing, such as when a moment load from wind or seismic forces accompanies the axial column load. Terzaghi’s original formula assumes concentric loading. For eccentric conditions, use Meyerhof’s effective area method: compute the effective footing dimensions as B’ = B minus 2eB and L’ = L minus 2eL, where eB and eL are the eccentricities of the resultant load in each direction. Use B’ and L’ in all bearing capacity calculations and in the area computation for applied pressure. The maximum eccentricity in any direction should not exceed one-sixth of the footing dimension (the kern condition) to avoid tension at the footing-soil interface, which most soils cannot sustain.

When phi = 0 degrees is entered (the total stress or undrained analysis case for saturated clays loaded rapidly), the calculator uses Terzaghi’s special-case bearing capacity factors: Nc = 5.14, Nq = 1.0, and Ngamma = 0.0. This is Skempton’s undrained bearing capacity solution for phi = 0 soils, and the cohesion input should be the undrained shear strength Su from an ASTM D2166 unconfined compression test or an ASTM D4767 consolidated undrained triaxial test. For this case, all the bearing capacity comes from the cohesion term, and the surcharge term contributes a constant offset equal to the overburden pressure. The self-weight term is zero because there is no frictional resistance in the failure wedge when phi = 0.

Terzaghi’s equations have several important limitations. They assume a rigid, rough footing base (meaning the soil does not slide under the footing), homogeneous soil from the footing base to a depth of at least 2B, and a horizontal ground surface. They also assume static loading and do not account for seismic conditions, cyclic loads, or dynamic effects. The equations are derived for shallow foundations where the depth-to-width ratio (Df/B) is 1.0 or less. For deeper footings (Df/B greater than 1.0), use Meyerhof’s depth correction factors. The formula also does not address settlement: a footing can be adequate in bearing capacity but still cause unacceptable settlement in compressible clays, which requires a separate consolidation analysis.

For routine shallow foundations under concentric loading on level ground, Terzaghi is the standard US approach and is conservative enough to be safe on most soil conditions. Meyerhof’s method adds shape, depth, and inclination correction factors and is preferred when the load is inclined, the footing is significantly deeper than it is wide (Df/B greater than 1.0), or the ground surface is sloped. Vesic’s method uses similar correction factors to Meyerhof but with slightly different Ngamma and is preferred by many structural engineering firms for their internal calculation standards. All three methods will give results within 15 to 25 percent of each other for standard conditions. Your project’s geotechnical engineer will specify which method to use in the geotechnical report, and that method should govern the final design.

No. Terzaghi’s bearing capacity equations apply exclusively to shallow foundations where the depth-to-width ratio (Df/B) is approximately 1.0 or less. Deep foundations such as driven piles, drilled shafts, and micropiles develop their capacity through a completely different mechanism: side friction along the shaft length plus end bearing at the tip, both of which depend on the soil properties at depth rather than at the surface. For driven pile capacity, use our Pile Driving ENR Formula Calculator for a dynamic estimate, or use static pile capacity methods per FHWA NHI-16-009 for final design. Drilled shaft capacity follows FHWA GEC-010, which uses separate alpha and beta methods for side friction.

The unit weight input in this calculator is the unit weight of the soil surrounding and beneath the footing, not the concrete. Use the soil’s total (moist) unit weight from the geotechnical report, typically 95 to 130 pcf for most US soils. The weight of the concrete footing itself is typically not included in the Terzaghi bearing capacity calculation because it is usually assumed to be approximately equal to the weight of soil it displaces (concrete weighs 150 pcf versus soil at 110 to 130 pcf), making the net additional load from the footing relatively small. However, the net footing weight above subgrade should be included in the applied load P when computing actual foundation pressure for the adequacy check.

Yes, in virtually all US jurisdictions. Building permits for structures subject to IBC require that foundation designs be prepared or reviewed and signed by a licensed professional engineer (PE) registered in the state where the project is located. This calculator provides preliminary analysis for estimating purposes, field checking, and educational use. The results cannot substitute for a site-specific geotechnical investigation report prepared by a licensed geotechnical engineer, or for foundation design plans sealed by a licensed structural PE. For residential projects exempt from engineering requirements in your jurisdiction, always confirm compliance with local building codes and the applicable version of IBC or IRC before using any calculated bearing capacity value in a permit application.

Terzaghi’s formulas assume a single, homogeneous soil layer from the footing base to at least twice the footing width below the base. In real US sites, multiple distinct soil strata are common, especially in coastal plains, river valleys, and post-glacial regions of the upper Midwest and Northeast. For layered soils, the geotechnical engineer selects the governing parameters based on the weakest layer within the failure zone (typically one to two footing widths below the base). If a weak layer exists just below the footing but a stronger layer is immediately beneath it, Meyerhof and Hanna’s punching shear method for layered soils is more appropriate than Terzaghi’s standard formula. For significant layering, request that the project geotechnical engineer perform the layered soil analysis rather than using a single-layer online tool.