Soil Bearing Capacity Calculator
Estimate soil bearing capacity for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Calculator
Adjust values & calculateCapacity Breakdown (Strip Footing)
Formula
The Terzaghi bearing capacity equation calculates the ultimate bearing capacity (qu) as the sum of three terms: the cohesion term (c times Nc), the surcharge/depth term (unit weight times foundation depth times Nq), and the width term (0.5 times unit weight times foundation width times Ngamma). The bearing capacity factors Nc, Nq, and Ngamma depend on the soil friction angle. The allowable bearing capacity is the ultimate value divided by the factor of safety (typically 3).
Last reviewed: December 2025
Worked Examples
Example 1: Strip Footing on Sandy Soil
Example 2: Square Footing for Column
Background & Theory
The Soil Bearing Capacity Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ the permanent self-weight of structural elements, finishes, and fixed equipment โ and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ0.45 typically yields concrete with 28-day compressive strengths of 30โ40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ350 MPa for mild steel) and ultimate tensile strength (typically 400โ500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.
History
The history behind the Soil Bearing Capacity Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ a mixture of volcanic ash, lime, and seawater โ enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ including the 1971 San Fernando and 1994 Northridge events โ drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.
Frequently Asked Questions
Formula
qu = c*Nc + gamma*Df*Nq + 0.5*gamma*B*Ngamma (Terzaghi)
The Terzaghi bearing capacity equation calculates the ultimate bearing capacity (qu) as the sum of three terms: the cohesion term (c times Nc), the surcharge/depth term (unit weight times foundation depth times Nq), and the width term (0.5 times unit weight times foundation width times Ngamma). The bearing capacity factors Nc, Nq, and Ngamma depend on the soil friction angle. The allowable bearing capacity is the ultimate value divided by the factor of safety (typically 3).
Worked Examples
Example 1: Strip Footing on Sandy Soil
Problem: Calculate the bearing capacity for a 4 ft wide strip footing at 3 ft depth in soil with cohesion 500 psf, friction angle 30 degrees, and unit weight 120 pcf.
Solution: Nq = e^(pi*tan30) x tan^2(60) = 18.40\nNc = (18.40-1)/tan(30) = 30.14\nNgamma = 2(18.40+1)tan(30) = 22.40\nqu = 500(30.14) + 120(3)(18.40) + 0.5(120)(4)(22.40)\nqu = 15,070 + 6,624 + 5,376 = 27,070 psf\nAllowable = 27,070 / 3 = 9,023 psf
Result: Ultimate = 27,070 psf, Allowable = 9,023 psf (FOS=3)
Example 2: Square Footing for Column
Problem: Determine the maximum column load for a 4 ft x 4 ft square footing using the same soil parameters.
Solution: qu_sq = 1.3(500)(30.14) + 120(3)(18.40) + 0.4(120)(4)(22.40)\nqu_sq = 19,591 + 6,624 + 4,301 = 30,516 psf\nAllowable = 30,516 / 3 = 10,172 psf\nMax load = 10,172 x 4 x 4 = 162,752 lbs
Result: Allowable = 10,172 psf, Max column load = 162,752 lbs (81.4 tons)
Frequently Asked Questions
What is soil bearing capacity and why is it important?
Soil bearing capacity is the maximum pressure that the soil beneath a foundation can sustain without experiencing shear failure or excessive settlement. It determines the size of footings and foundations needed to safely support structural loads. If the applied pressure exceeds the bearing capacity, the soil undergoes shear failure, causing the foundation to sink, tilt, or punch through the ground. Bearing capacity depends on soil type, strength parameters, foundation dimensions, and depth of embedment.
What are the Terzaghi bearing capacity factors Nc, Nq, and Ngamma?
The Terzaghi bearing capacity factors are dimensionless parameters that depend on the soil friction angle. Nc is the cohesion factor representing the contribution of soil cohesion to bearing capacity. Nq is the surcharge factor accounting for the overburden pressure from soil above the foundation level. Ngamma is the self-weight factor representing the contribution of soil weight in the failure zone below the foundation. These factors increase dramatically with friction angle, meaning dense granular soils have much higher bearing capacities.
What factor of safety is used for bearing capacity design?
A factor of safety of 3.0 is standard for most bearing capacity design under normal loading conditions. This accounts for variability in soil properties, simplifications in the bearing capacity theory, and uncertainties in the applied loads. For temporary structures, a FOS of 2.0 to 2.5 may be acceptable. When loads include wind or seismic components, many codes allow a one-third increase in allowable bearing pressure. The allowable bearing capacity equals the ultimate bearing capacity divided by the factor of safety.
How does foundation depth affect bearing capacity?
Increasing foundation depth generally increases bearing capacity because the overburden soil above the foundation level provides additional resistance to shear failure through the Nq term. The surcharge effect equals the soil unit weight multiplied by the depth multiplied by Nq. For a soil with friction angle of 30 degrees, doubling the foundation depth from 3 to 6 feet can increase the ultimate bearing capacity by 20 to 30 percent. However, deeper excavation increases construction costs, so the optimal depth balances structural requirements with economy.
What are typical bearing capacity values for different soil types?
Presumptive allowable bearing capacities from building codes provide rough guidance: soft clay 1,000 to 2,000 psf, medium clay 2,000 to 4,000 psf, stiff clay 4,000 to 6,000 psf, loose sand 2,000 to 3,000 psf, medium dense sand 3,000 to 5,000 psf, dense sand 5,000 to 8,000 psf, gravel 6,000 to 12,000 psf, and bedrock 10,000 to 100,000 psf. These are conservative estimates for preliminary design and should be verified with site-specific geotechnical investigation.
How do I calculate the load-bearing capacity of a beam?
Beam capacity depends on material, cross-section dimensions, span length, and support conditions. For a simple rectangular wood beam, bending strength = (F_b x b x d^2) / 6, where F_b is allowable stress, b is width, and d is depth. Always consult a structural engineer for critical applications.
References
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