Introduction
The footing-sizing formula is famously short – width = load / allowable bearing pressure – but it condenses a century of geotechnical theory. Behind the allowable pressure sits Terzaghi’s bearing capacity equation, soil shear strength, and a factor of safety; behind the load sits the entire structural analysis of the building. Understanding each layer helps you spot bad inputs, sanity-check results, and know exactly where the calculator’s job ends and the engineer’s begins.
The Soil Bearing Capacity Calculator applies the sizing formulas in this guide – strip footing width, pad footing area, and unit conversions – in both imperial and metric. This article derives each step, explains every variable, and works the numbers twice (once per unit system) so you can verify the calculator against hand math. All design decisions still belong to a licensed geotechnical or structural engineer.
Layer 1: Ultimate Bearing Capacity (Terzaghi)
In 1943, Karl Terzaghi published the bearing capacity equation that still underlies foundation practice:
q_ult = c * Nc + q * Nq + 0.5 * gamma * B * N_gamma
Each term is a physical contribution to the soil’s strength:
- c (cohesion) – the soil’s stickiness, from clay content; zero for clean sands and gravels.
- q (overburden pressure) – the weight of soil above footing depth: depth * unit weight. Deeper footings start stronger.
- gamma (unit weight) – the soil’s density, roughly 110-130 lb/ft3 (17-20 kN/m3) for typical soils.
- B (footing width) – wider footings mobilize more soil, so capacity grows with width.
- Nc, Nq, N_gamma (bearing capacity factors) – dimensionless numbers driven by the soil’s friction angle (phi). Higher phi means dramatically higher factors – this is why dense gravel out-carries loose sand so decisively.
You will almost never compute this yourself – the geotechnical engineer does, using lab or field test data for c and phi. How soil type feeds these factors is covered in the material guide. What matters for you: the ultimate capacity is a failure load, and it depends on soil properties that vary across your site. That variability is exactly why the next layer exists.
Layer 2: From Ultimate to Allowable
q_a = q_ult / FS
where FS is the factor of safety, typically 2.5 to 3.0 for foundations. The factor of safety covers soil variability, load uncertainty, and the difference between shear failure and excessive settlement – a footing can be “safe” from collapse yet settle enough to crack walls, so allowable pressure is also settlement-limited.
The practical rule this creates: never divide an allowable value by a safety factor again. Geotechnical reports and code tables quote q_a with FS already applied. Double-applying it doesn’t add safety – it adds concrete. This is one of the most common and expensive errors; see the common mistakes guide.
Layer 3: Sizing the Footing
Assembling an honest load is half the battle – the estimating guide walks through load buildup and tributary widths step by step.
Strip footings (walls)
Consider one linear foot of wall. It carries w (lb/ft) and bears on a strip B (ft) wide, so the contact pressure is w / B. Setting contact pressure equal to the allowable pressure and solving:
B = w / q_a
Worked: w = 4,000 lb/ft, q_a = 1,500 psf. B = 4,000 / 1,500 = 2.667 ft (round up to 2 ft 8 in, i.e., 32 in).
Metric: w = 58.4 kN/m, q_a = 71.8 kPa. B = 58.4 / 71.8 = 0.813 m. Cross-check: 2.667 ft * 0.3048 = 0.813 m. The two systems agree exactly, as they must.
Square pad footings (columns)
A column delivers a point load P (lb) onto a square of side S (ft). Contact pressure is P / S^2, so:
S = sqrt(P / q_a)
Worked: P = 30,000 lb, q_a = 2,000 psf. Area = 30,000 / 2,000 = 15 ft2; S = sqrt(15) = 3.87 ft (round up to 4 ft 0 in).
Metric: P = 133.4 kN (30,000 lb * 4.44822 N/lb), q_a = 95.8 kPa. Area = 133.4 / 95.8 = 1.393 m2; S = sqrt(1.393) = 1.18 m. Cross-check: 3.87 ft * 0.3048 = 1.18 m.
Rectangular footings
Same pressure equation, two unknowns: L * W = P / q_a. Choose one dimension to fit the geometry (a property line, an existing wall), then solve for the other. The calculator’s square-footing mode gives the area; you proportion it.
Layer 4: Unit Conversions, Done Right
Unit errors are the silent killers of footing math. The exact factors:
- Pressure: 1 psf = 0.0478803 kPa. So 1,500 psf = 71.8 kPa; 2,000 psf = 95.8 kPa; 3,000 psf = 143.6 kPa.
- Line load: 1 lb/ft = 0.0145939 kN/m. So 4,000 lb/ft = 58.4 kN/m.
- Point load: 1 lb = 4.44822 N, so 1,000 lb (1 kip) = 4.448 kN.
- Length: 1 ft = 0.3048 m; 1 in = 25.4 mm.
The verification habit: run every calculation in both systems. If 2.667 ft doesn’t equal 0.813 m, a conversion went wrong somewhere – catch it on paper, not in concrete. A frequent trap is the kip: structural loads are often quoted in kips (1 kip = 1,000 lb). Entering “30” meaning 30 kips as 30 lb undersizes the footing by a factor of 1,000.
What the Formula Assumes (and When It Breaks)
B = w / q_a is exact only under its assumptions. Know them:
- Uniform pressure. Real footings see eccentric loads and moments; engineers check maximum edge pressure against q_a, not just the average.
- Homogeneous soil. A weak layer below footing depth can govern. The formula checks the bearing surface, not what’s beneath it.
- Static, vertical load. Wind, seismic, and lateral loads need separate analysis.
- Normal moisture. Saturation, flooding, and seasonal water table swings reduce capacity below the number you used.
- No adjacent excavation. Digging beside a footing removes the confining soil the capacity depends on.
Each broken assumption is a reason the number needs an engineer’s review, not a reason to abandon the formula – the formula sizes the footing, and the engineer verifies the conditions. How those verifications map to code requirements is covered in the code compliance guide.
Related Guides
- Complete Guide – the full overview: terms, formulas, worked example.
- Estimating Guide – building loads and footing takeoffs step by step.
- Material (Soil Type) Guide – how soil type feeds the capacity factors.
- Pro Tips – field judgment that keeps the math honest.
- FAQ – quick answers on units, safety factors, and conversions.
Frequently Asked Questions
What is the basic footing width formula?
For a strip footing: width = load per linear foot / allowable bearing pressure. For a square pad footing: side = square root of (total load / allowable bearing pressure).
What is Terzaghi’s bearing capacity equation?
q_ult = c*Nc + q*Nq + 0.5*gamma*B*N_gamma. It computes the soil’s ultimate (failure) capacity from cohesion, overburden, soil weight, footing width, and bearing capacity factors. Geotechnical engineers use it to derive the allowable pressure you design with.
What factor of safety is used for bearing capacity?
Typically 2.5 to 3.0. Allowable values in reports and code tables already include it – do not apply it a second time.
How many kPa is 1,500 psf?
71.8 kPa (multiply psf by 0.04788).
Why do imperial and metric results sometimes disagree slightly?
Rounding in intermediate conversions. Carry full precision through the calculation and round only the final dimension; the worked examples above show exact agreement (2.667 ft = 0.813 m).
Get Your Number
The chain is short: Terzaghi gives the ultimate capacity, the factor of safety gives the allowable pressure, and division by the load gives the footing size. The Soil Bearing Capacity Calculator runs the last two links in both unit systems – verify it against the hand calculations above, then take the result to the engineer who owns the first link.
Disclaimer: Formulas shown are for planning and educational purposes. Soil capacity varies by site, moisture, depth, and loading conditions – verify with your local building code and a site-specific geotechnical report, and consult a licensed geotechnical or structural engineer for foundation design.
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