Bearing Capacity Calculator

The Bearing Capacity Calculator estimates how much load a shallow footing can carry on soil before the ground beneath it fails. It reports the ultimate bearing pressure, the allowable bearing pressure after your factor of safety, the allowable capacity of the footing, and the utilisation of that capacity by the load you enter. It also suggests the smallest footing width from a fixed list of candidate sizes that would carry the load.

It covers strip, square, rectangular and circular footings, and works entirely in SI units: metres for lengths, kilopascals for pressures, kilonewtons for loads, and kilonewtons per cubic metre for soil unit weight.

Use it for a first-pass check or for teaching. It is not a foundation design. The soil strength values it needs must come from a site-specific geotechnical investigation, and the failure modes it does not model can govern. Foundation design must be carried out, and where required sealed, by a licensed geotechnical or civil engineer working to the code adopted where the work is built.

Purpose and model boundary

This model estimates the ultimate and allowable axial capacity of a shallow footing. It derives the bearing-capacity factors from the entered friction angle, applies shape and depth factors for the selected footing geometry, divides the ultimate pressure by the chosen factor of safety, and compares the resulting capacity with the applied load. It is a preliminary geotechnical check, not a foundation design.

The spreadsheet is the calculation authority. The page sends the named inputs to the calculation service and displays the workbook's returned results and status; no geotechnical equation is reimplemented in browser code.

Inputs and units

The rectangular length is used only for a rectangular footing. Circular area is πB²/4; square area is B²; a strip uses B × 1 m; and rectangular area is BL.

Governing relationships

With φ in radians, the workbook derives:

• Nq = exp(π tan φ) × tan²(45° + φ/2);
• Nc = (Nq − 1) / tan φ, with the workbook's limiting clay value used at φ = 0;
• Vesic Nγ = 2(Nq + 1)tan φ, or Meyerhof Nγ = (Nq − 1)tan(1.4φ).

The gross ultimate pressure follows the three-term bearing-capacity form

qult = cNc sc dc + γDf Nq sq dq + 0.5γB Nγ sγ dγ,

where the shape and depth factors are selected from the workbook's formula branches. Then qallow = qult / FS, Qallow = qallow × plan area, and utilisation = P / Qallow. The required width is selected from the workbook's bounded trial-width series; it is a diameter for a circular footing and a width per metre of run for a strip.

Calculation sequence

1. Validate the shape, dimensions, soil parameters, factor method and factor of safety.
2. Derive Nc, Nq and Nγ from φ.
3. Apply the geometry-specific area, shape factors and depth factors.
4. Calculate ultimate pressure, allowable pressure, allowable capacity and utilisation.
5. Evaluate the trial-width series and plot allowable capacity against width.
6. Return the workbook's status before the results are interpreted.

Outputs and interpretation

Allowable bearing pressure is a pressure limit; allowable axial capacity includes the selected footing area. Utilisation above 1 means the entered demand exceeds the workbook's allowable capacity. Required width is a discrete sizing guide within the workbook's search range, not a final optimized design. The individual bearing factors are exposed so the selected reference method can be checked.

Validation and status logic

The workbook returns named states including:

Assumptions and limitations

• Soil is represented by uniform c, φ and γ values from a site investigation.
• The footing is shallow, centrally and vertically loaded, and uses the workbook's idealized strip, square, rectangular or circular branch.
• Groundwater correction, eccentric or inclined loading, layered soil, settlement, punching, sliding, uplift, seismic effects and interaction with nearby foundations are not modeled.
• The Nγ value varies among published methods; the selected method must match the governing design reference.
• The trial-width result is bounded and discrete. A blank result can mean that the search completed without finding a qualifying candidate.

Restrictions and non-computing states

This calculator restricts selectors to the workbook's declared lists and prevents values outside published numeric bounds from being submitted. A workbook NOT VALID result supersedes displayed numerical residues. Strip results use per-metre units and must not be compared directly with pad-footing totals.

Errors and warnings

A rejected entry means the request did not satisfy the published input rules. NOT VALID means the workbook refused the calculation state. CHECK means calculations were produced but capacity, search coverage or an engineering condition requires review. A calculation-service failure is an availability problem, not a geotechnical conclusion.

The workbook derives its bearing capacity factors rather than reproducing any table from a standard. The published sources for the forms it implements are below.

• Vesic, A. S. Analysis of Ultimate Loads of Shallow Foundations. Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, volume 99, number 1, 1973, pages 45 to 73. https://doi.org/10.1061/JSFEAQ.0001846 (the Vesic N-gamma form and the shape factors used here)
• Meyerhof, G. G. Some Recent Research on the Bearing Capacity of Foundations. Canadian Geotechnical Journal, volume 1, number 1, 1963, pages 16 to 26. https://doi.org/10.1139/t63-003 (the alternative Meyerhof N-gamma form offered by the method selector)
• Hansen, J. Brinch. A Revised and Extended Formula for Bearing Capacity. Danish Geotechnical Institute, Bulletin Number 28, Copenhagen, 1970. (the depth factors used here)
• Wikipedia. Bearing capacity. https://en.wikipedia.org/wiki/Bearing_capacity

Soil parameters shipped with the workbook are illustrative and carry no authority. Values for design must come from a site-specific geotechnical investigation.

Additional source notes migrated from Methodology

The workbook implements derived shallow-foundation bearing-capacity relationships and documents the chosen Nγ method in its References sheet. Site-specific parameters, the governing design standard and review by a licensed geotechnical engineer control real foundation design.