Soil Bearing Capacity Calculator
Calculate ultimate and allowable soil bearing capacity using Terzaghi's bearing capacity equation
Soil Properties
Foundation Parameters
Results
Bearing Capacity Factors
30.14
18.40
22.40
Ultimate Bearing Capacity (qu)
1653.57 kN/m²
Allowable Bearing Capacity (qa)
551.19 kN/m²
Formula Used
qu = c·Nc + γ·Df·Nq + 0.5·γ·B·Nγ (Terzaghi's Equation)
What is Soil Bearing Capacity?
Soil bearing capacity is the maximum pressure that soil can safely support without experiencing shear failure or excessive settlement. It is one of the most critical parameters in foundation engineering because it determines the size and depth of footings, piles, and other foundation elements. If a foundation applies pressure exceeding the soil's bearing capacity, the soil will fail in shear, causing the structure to settle excessively, tilt, or even collapse.
Bearing capacity is expressed in units of pressure — kilopascals (kPa) in SI units or pounds per square foot (psf) in US customary units. The ultimate bearing capacity is the theoretical maximum pressure the soil can support before failure. The allowable bearing capacity is the ultimate capacity divided by a factor of safety (typically 3) to provide a margin of safety against uncertainties in soil properties, loading conditions, and construction methods.
This calculator implements Terzaghi's bearing capacity equation for strip footings, one of the most widely used methods in geotechnical engineering. It computes the bearing capacity factors (Nc, Nq, and N-gamma) from the soil friction angle, calculates the ultimate bearing capacity considering cohesion, surcharge, and wedge effects, and divides by the factor of safety to obtain the allowable bearing capacity for foundation design.
Terzaghi's Bearing Capacity Equation
Terzaghi's equation for the ultimate bearing capacity of a strip footing on the surface of a soil is a classical formula that accounts for three sources of soil resistance: cohesion along the failure surface, surcharge from the soil above the foundation level, and the weight of the soil wedge below the footing.
Terzaghi's Bearing Capacity Equation
Where:
- qu= Ultimate bearing capacity (kN/m² or psf)
- c= Soil cohesion (kN/m² or psf)
- γ= Unit weight of soil (kN/m³ or pcf)
- Df= Depth of foundation below ground surface (m or ft)
- B= Width of the foundation (m or ft)
- Nc, Nq, Nγ= Bearing capacity factors that depend on the friction angle phi
Bearing Capacity Factors
The bearing capacity factors Nc, Nq, and N-gamma are functions of the soil's internal friction angle (phi). They increase rapidly with friction angle, reflecting the dramatic increase in bearing capacity as soil becomes denser and more frictional:
| Friction Angle (phi) | Nc | Nq | Nγ |
|---|---|---|---|
| 0 degrees (soft clay) | 5.7 | 1.0 | 0.0 |
| 20 degrees | 17.7 | 7.4 | 5.0 |
| 30 degrees | 30.1 | 18.4 | 22.4 |
| 40 degrees | 75.3 | 64.2 | 109.4 |
How to Use This Calculator
Enter the following soil and foundation parameters to compute the bearing capacity:
- Cohesion (c): The soil's cohesive strength in kN/m². For soft clay, use 10–25 kN/m²; for stiff clay, use 50–100 kN/m². For sands, cohesion is approximately 0.
- Friction Angle (phi): The internal friction angle in degrees. Typically 25–35 degrees for sands, 0–10 degrees for clays.
- Unit Weight (gamma): The total unit weight of the soil in kN/m³. Typical values range from 16 to 22 kN/m³ depending on soil type and density.
- Foundation Width (B): The width of the footing in meters. Wider footings mobilize more soil resistance and have higher bearing capacity.
- Foundation Depth (Df): The depth below ground surface to the base of the footing in meters.
- Factor of Safety: Typically 3.0 for standard foundations. Use 2.5 for temporary structures or 4.0 for critical structures.
- Review Results: The calculator displays the bearing capacity factors, ultimate bearing capacity, and allowable bearing capacity.
Interpreting the Results
The allowable bearing capacity (qa) is the maximum pressure that can be applied to the soil at the foundation level without causing shear failure, after applying the factor of safety. This value is used to size the footing: the required footing area equals the column load divided by the allowable bearing capacity. For example, if the column load is 500 kN and qa is 200 kN/m², the footing area must be at least 2.5 m².
It is important to note that bearing capacity addresses shear failure, but settlement is often the controlling design criterion for foundations on soft or compressible soils. A soil may have adequate bearing capacity but still experience excessive settlement under load. For detailed foundation design, both bearing capacity and settlement analyses should be performed, and the more restrictive criterion controls the design.
The water table also affects bearing capacity. If the water table is close to the foundation level, the effective unit weight of the soil is reduced by the buoyancy of water, which decreases the bearing capacity. The current calculator uses the full unit weight; for projects near the water table, consult a geotechnical engineer for a more refined analysis.
Real-World Applications
Soil bearing capacity calculations are the starting point for the design of every building foundation. Shallow foundations (footings, mats, and rafts) transfer building loads directly to the soil at or near the surface, and their size is governed by the allowable bearing capacity. Deep foundations (piles and caissons) transfer loads to deeper, stronger soil layers when surface soils are too weak to support the structure.
Typical bearing capacity values for common soils range from 50–100 kN/m² for soft clays to 300–600 kN/m² for dense gravels and weathered rock. Accurate bearing capacity data comes from field tests (Standard Penetration Test, Cone Penetration Test) and laboratory testing (triaxial test, direct shear test) performed by geotechnical engineers. This calculator provides preliminary estimates for preliminary design and educational purposes.
Worked Examples
Sandy Soil Foundation
Problem:
Calculate the allowable bearing capacity for a 2-meter wide strip footing at 1.5 m depth in medium-dense sand with phi = 30 degrees, c = 0 kN/m², gamma = 18 kN/m³, and safety factor = 3.
Solution Steps:
- 1Convert phi to radians: 30 degrees = 0.5236 radians
- 2Bearing capacity factors: Nq = exp(pi × tan(30)) × tan^2(45 + 30/2) = 18.4, Nc = (18.4 - 1) / tan(30) = 30.1, N-gamma = 2 × (18.4 + 1) × tan(30) = 22.4
- 3Ultimate capacity: qu = 0 × 30.1 + 18 × 1.5 × 18.4 + 0.5 × 18 × 2 × 22.4 = 0 + 496.8 + 403.2 = 900 kN/m²
- 4Allowable capacity: qa = 900 / 3 = 300 kN/m²
Result:
Allowable bearing capacity = 300 kN/m² (approximately 6,260 psf)
Clay Soil Foundation
Problem:
A 1.5-meter wide footing at 1 m depth in stiff clay with c = 75 kN/m², phi = 0 degrees, gamma = 20 kN/m³, safety factor = 3.
Solution Steps:
- 1Bearing capacity factors for phi = 0: Nc = 5.7, Nq = 1.0, N-gamma = 0
- 2Ultimate capacity: qu = 75 × 5.7 + 20 × 1.0 × 1.0 + 0 = 427.5 + 20 = 447.5 kN/m²
- 3Allowable capacity: qa = 447.5 / 3 = 149.2 kN/m²
- 4For a 500 kN column load, required footing width: B = 500 / (149.2 × 1) = 3.35 m
Result:
Allowable bearing capacity = 149.2 kN/m², required footing width for 500 kN load = 3.35 m
Effect of Foundation Width
Problem:
Compare bearing capacity for 1 m, 2 m, and 3 m wide footings in dense sand with phi = 35 degrees, c = 0, gamma = 20 kN/m³, Df = 1.5 m.
Solution Steps:
- 1For phi = 35: Nq = 33.3, N-gamma = 37.7
- 2B = 1 m: qu = 0 + 20 × 1.5 × 33.3 + 0.5 × 20 × 1 × 37.7 = 999 + 377 = 1,376 kN/m²
- 3B = 2 m: qu = 999 + 0.5 × 20 × 2 × 37.7 = 999 + 754 = 1,753 kN/m²
- 4B = 3 m: qu = 999 + 0.5 × 20 × 3 × 37.7 = 999 + 1,131 = 2,130 kN/m²
Result:
Wider footings have higher bearing capacity: 1,376, 1,753, and 2,130 kN/m² for 1 m, 2 m, and 3 m widths
Tips & Best Practices
- ✓Always obtain a geotechnical report before designing foundations for new construction.
- ✓Bear in mind that settlement, not bearing capacity, often controls the design on soft soils.
- ✓A high water table can dramatically reduce bearing capacity — account for buoyancy effects.
- ✓Wider footings have higher bearing capacity because they mobilize a larger soil wedge.
- ✓Increasing foundation depth generally increases bearing capacity due to greater surcharge.
- ✓For cohesive soils, short-term (undrained) and long-term (drained) bearing capacities differ significantly.
Frequently Asked Questions
Sources & References
Last updated: 2026-06-06
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: Standard Mathematical References
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