Soil Bearing Capacity Formula: Calculations and Bearing Pressure

Soil bearing capacity is one of the most important considerations in foundation design because the ground beneath a structure must safely support the loads transferred through its foundation.

In simple terms, the load bearing capacity of soil describes how much pressure the ground can support without experiencing unacceptable shear failure or settlement. However, bearing capacity is not determined by soil type alone. Foundation width, foundation depth, soil strength, groundwater conditions, footing shape, loading conditions and the design method can all affect the result.

A commonly used general form of the bearing capacity equation for a shallow foundation is:

For the simpler form of the equation, where correction factors are not explicitly included:

q_u = c′N_c + γD_fN_q + ½γBN_γ

Where:

• q_u = ultimate bearing capacity
• c′ = effective cohesion of the soil
• γ = effective or appropriate unit weight of soil
• D_f = foundation embedment depth
• B = footing width
• N_c, N_q, N_γ = bearing capacity factors related primarily to the soil friction angle, depending on the selected theory
• s = shape factors
• d = depth factors
• i = load inclination factors
• b = foundation-base inclination factors
• g = ground-slope inclination factors

The exact equation and factors used should match the geotechnical design method and the project conditions. Modern foundation design also considers serviceability, particularly settlement, rather than checking shear capacity alone.

Important: This article is an educational guide to the soil bearing capacity formula and load bearing capacity. A real building foundation should be designed using site-specific geotechnical information and the applicable design standard by a qualified engineer.

Summary: Key Takeaways on Soil Bearing Capacity

• Soil bearing capacity is fundamental to safe foundation design.
• Load bearing capacity depends on soil strength, foundation dimensions, embedment, groundwater and loading conditions.
• The ultimate bearing capacity represents the calculated resistance associated with a limiting ground failure condition.
• The allowable bearing pressure is lower and reflects the adopted design safety approach and, where applicable, serviceability requirements.
• Settlement can control foundation design even when the calculated shear bearing capacity appears adequate.
• Groundwater can affect effective stresses and therefore the calculated bearing resistance.
• Soil investigation and appropriate laboratory or in-situ testing are important for obtaining reliable design parameters.
• Low-capacity ground may require wider footings, ground improvement, raft foundations or deep foundations depending on the project.

For a broader discussion of foundation selection and soil investigation, see our guide to building foundations and foundation design.

1. What Is the Bearing Capacity of Soil?

The bearing capacity of soil is the ability of the ground beneath a foundation to resist the pressure transferred from the structure without reaching an unacceptable failure condition.

In foundation engineering, two ideas are particularly important:

1. Ultimate or bearing resistance: the resistance associated with a limiting ground failure condition.
2. Serviceability: whether the foundation and structure experience acceptable settlement, rotation or movement while carrying the intended loads.

This means that saying a soil has a particular “load bearing capacity” without stating the foundation size, depth, loading condition and design basis can be misleading.

For example, the same soil may support different pressures beneath a narrow strip footing, a square pad footing and a large raft foundation because foundation geometry and stress distribution are different.

Groundwater can also change the effective stress conditions used in an analysis. Bearing-capacity calculations therefore need to consider the actual site conditions rather than relying only on a generic soil table.

Why Soil Bearing Capacity Matters

If the foundation pressure is too high for the ground conditions, the soil may experience bearing resistance failure or excessive deformation. The resulting problems can include:

• uneven settlement;
• foundation rotation;
• cracking in walls and finishes;
• floor distortion;
• loss of structural serviceability;
• in severe cases, ground or foundation failure.

For this reason, load bearing capacity should always be considered together with settlement and the overall geotechnical design.

2. What Is the Soil Bearing Capacity Formula?

For shallow foundations, one commonly encountered form of the bearing capacity equation is based on the classical work of Terzaghi and later developments by Meyerhof, Hansen and Vesic.

The simplified equation can be written as:

q_u = c′N_c + γD_fN_q + ½γBN_γ

The three terms represent the contributions associated with:

• cohesion: c′N_c
• foundation embedment: γD_fN_q
• soil self-weight beneath the footing: ½γBN_γ

In a more complete analysis, shape, depth, load inclination, base inclination and ground-slope factors may be introduced.

This is why two engineers can obtain different results from what appears to be the “same” bearing capacity equation if they use different theories, correction factors or design assumptions.

What Do the Bearing Capacity Factors Mean?

The values of these factors depend on the adopted theory and the soil friction angle. They should therefore not be selected from an arbitrary table without identifying the design method.

3. Generalized Bearing Capacity Equation

For more realistic foundation conditions, the equation can be expanded to include correction factors:

q_u = c′N_cs_cd_ci_cb_cg_c + γD_fN_qs_qd_qi_qb_qg_q + ½γBN_γs_γd_γi_γb_γg_γ

Where:

• s_c, s_q, s_γ = shape factors
• d_c, d_q, d_γ = foundation depth factors
• i_c, i_q, i_γ = load inclination factors
• b_c, b_q, b_γ = foundation-base inclination factors
• g_c, g_q, g_γ = ground-slope factors

Not every factor is required in every project. For a centrally loaded footing with a level base and level surrounding ground, some correction factors may be taken as unity under the selected design method.

Modern geotechnical guidance emphasizes that the foundation design should consider the relevant limit states, including bearing resistance failure, sliding, overall stability and excessive settlement.

4. Worked Example: Bearing Capacity of Cohesive Clay

Let us use a simplified example to demonstrate how the soil bearing capacity formula works.

Given Data

• Footing width, B: 1.5 m
• Foundation depth, D_f: 1.2 m
• Unit weight, γ: 18 kN/m³
• Cohesion, c: 30 kPa
• Friction angle, φ: 0°
• N_c: 5.7
• N_q: 1.0
• N_γ: 0

For this simplified φ = 0° calculation:

q_u = cN_c + γD_fN_q + ½γBN_γ

Substituting the values:

q_u = (30 × 5.7) + (18 × 1.2 × 1.0) + ½(18 × 1.5 × 0)

Therefore:

q_u = 192.6 kPa

Calculating an Illustrative Allowable Pressure

If an illustrative factor of safety of 3 is adopted for this simplified example:

q_allow = q_u / 3

Therefore:

q_allow = 192.6 / 3 = 64.2 kPa

This reproduces the original example’s 64.2 kPa value.

Important: The 64.2 kPa value should not be interpreted as a site-specific allowable bearing pressure. A real design requires appropriate soil parameters, groundwater conditions, footing geometry, load combinations, settlement assessment and the applicable design standard.

5. Applying a Factor of Safety

A traditional allowable-stress approach may express the relationship as:

q_allow = q_u / FS

Where:

• q_allow = allowable bearing pressure
• q_u = calculated ultimate bearing capacity
• FS = adopted factor of safety

However, it is important not to assume that every modern foundation design simply divides an ultimate value by 3. Modern limit-state design systems, including Eurocode 7, use design approaches and partial factors rather than relying exclusively on a single global factor of safety.

Therefore, the safety factor or partial factors should come from the applicable design code and the project’s geotechnical design basis.

6. Worked Example: Bearing Capacity of Dense Sand

For non-cohesive soil such as sand, cohesion may be approximated as zero in an appropriate drained analysis, while the friction angle becomes particularly important.

Given Data

• Footing width, B: 2.0 m
• Foundation depth, D_f: 1.5 m
• Unit weight, γ: 19 kN/m³
• Friction angle, φ: 35°
• Cohesion, c: 0
• N_c: 57.8
• N_q: 41.4
• N_γ: 42.4

Using the simplified equation:

q_u = cN_c + γD_fN_q + ½γBN_γ

Because c = 0:

q_u = (19 × 1.5 × 41.4) + ½(19 × 2.0 × 42.4)

The result is approximately:

q_u = 1,985.5 kPa

If a factor of safety of 3 were used purely for this illustrative allowable-stress calculation:

q_allow ≈ 661.8 kPa

Again, this is a simplified educational calculation. A square footing normally requires the appropriate shape factors under the selected bearing-capacity theory, and groundwater, eccentricity, footing stiffness, settlement and other factors can materially change the design result.

7. Ultimate Bearing Capacity, Safe Bearing Capacity and Allowable Bearing Pressure

These terms are related but should not be treated as interchangeable.

1. Ultimate Bearing Capacity

Ultimate bearing capacity, commonly represented as q_u, is associated with the limiting resistance of the ground under the foundation in the adopted bearing-capacity model.

It is commonly calculated from soil strength, foundation geometry, embedment and other relevant factors.

2. Safe or Allowable Bearing Capacity

In traditional allowable-stress terminology, a reduced value is obtained from the ultimate capacity using an adopted factor of safety:

q_safe = q_u / FS

In modern design, terminology and calculation procedures depend on the applicable code. Therefore, the phrase allowable bearing pressure should always be interpreted in the context of the design method being used.

3. Net Safe Bearing Capacity

Net bearing capacity considers the increase in pressure attributable to the foundation load relative to the existing overburden pressure at foundation level.

A simplified traditional relationship can be expressed as:

q_ns = (q_u / FS) − γD_f

But care is required because gross and net quantities must be kept consistent throughout the calculation. Mixing gross ultimate pressure with net allowable pressure can produce an incorrect foundation design.

8. Bearing Capacity vs. Load Bearing Capacity

The phrases bearing capacity and load bearing capacity are often used interchangeably in general construction discussions, but engineers should be more precise.

Bearing capacity is normally expressed as a pressure or stress, such as kPa.

Load, on the other hand, is a force, commonly expressed in kN.

The relationship is:

Load = Bearing Pressure × Foundation Area

For example, if a footing has an area of 4 m² and the design bearing pressure is 150 kPa:

Load = 150 kN/m² × 4 m² = 600 kN

This simplified relationship shows why increasing the footing area can reduce the average pressure imposed on the ground for a given structural load.

However, actual foundation design must also consider eccentric loading, contact-pressure distribution, footing self-weight, moments and other actions.

9. What Factors Affect the Load Bearing Capacity of Soil?

Several factors influence the calculated load bearing capacity of soil.

1. Soil Type

Clay, silt, sand, gravel, weathered rock and engineered fill can have very different strength and deformation characteristics.

Soil classification alone, however, is not enough to establish a safe foundation pressure. Density, strength parameters, stress history and drainage conditions can be equally important.

2. Soil Strength

For many bearing-capacity calculations, cohesion and the effective friction angle are fundamental parameters.

3. Foundation Width

Footing width affects the stress distribution and the bearing-capacity terms involving B. It can therefore affect the calculated capacity as well as the settlement response.

4. Foundation Depth

Embedment depth can increase confinement and affects the surcharge term in many bearing-capacity formulations.

5. Groundwater

Groundwater can influence effective stress and the unit weight used in the bearing-capacity calculation. In some conditions, groundwater corrections are required.

Geotechnical references specifically identify groundwater position relative to foundation level as a factor that can alter bearing-capacity calculations.

6. Footing Shape

A strip, rectangular, square and circular foundation does not necessarily have the same bearing response. Shape factors may therefore be required.

7. Load Inclination and Eccentricity

A footing carrying a vertical, centrally applied load is different from one subjected to significant moment, horizontal force or eccentric loading.

8. Ground Slope

Sloping ground can reduce bearing resistance and may introduce additional stability considerations.

9. Soil Layering

A strong layer over weak soil, weak material over dense sand, fill over natural soil, or alternating soil strata can significantly affect foundation performance.

10. Settlement

Even if the calculated ultimate bearing capacity is high, settlement can still control the foundation design.

This is an important distinction: load bearing capacity is not the same thing as settlement performance.

10. Why Settlement Matters as Much as Bearing Capacity

A foundation can theoretically remain below a calculated shear-failure capacity while still experiencing too much settlement for the building to perform properly.

Settlement may cause:

• cracks in masonry;
• distorted floors;
• sticking doors and windows;
• serviceability problems;
• uneven movement between different parts of a building;
• damage to finishes and services.

For this reason, modern geotechnical foundation design considers both ultimate limit states and serviceability limit states. Eurocode 7 guidance, for example, identifies bearing resistance failure and excessive settlement as separate foundation design considerations.

A settlement calculation may use soil stiffness, foundation dimensions, applied pressure, influence factors and other parameters rather than simply comparing pressure with a single allowable bearing value.

11. How Soil Type Influences Bearing Capacity

Cohesive Soil

Cohesive soils such as clay may exhibit significant cohesion, but their engineering behavior depends on drainage, stress history, plasticity, moisture and other properties.

Some clays can also undergo swelling and shrinkage when their moisture conditions change.

Granular Soil

Sand and gravel generally derive much of their shear strength from friction and particle interlock. Density and effective stress are therefore important.

Loose Sand

Loose granular soil can experience significant deformation under load and may require improvement or a different foundation strategy depending on the project.

Engineered Fill

Fill should not automatically be assumed to have the same properties as natural soil. Its suitability depends on the material, placement method, compaction and verification testing.

12. Common Bearing Capacity Failure Modes

Understanding failure mechanisms helps explain why the load bearing capacity of soil must be assessed carefully.

General Shear Failure

A well-defined failure surface develops beneath and around the footing, with significant ground movement as the ultimate resistance is approached.

Local Shear Failure

The soil develops a less clearly defined failure mechanism and experiences progressive deformation.

Punching Shear Failure

The footing may penetrate downward into a relatively weak or loose soil layer without developing the same broad failure surface associated with general shear.

Excessive Settlement

This is not necessarily the same as ultimate shear failure. A structure may become unacceptable because of excessive deformation before the soil reaches a theoretical ultimate failure condition.

Foundation design therefore needs to address both strength and deformation.

13. How Can You Increase the Load Bearing Capacity of Soil?

If investigation shows that the existing ground cannot adequately support the proposed structure, engineers have several possible strategies.

1. Soil Compaction

Compaction can increase density and improve the engineering properties of suitable granular and fill materials.

2. Soil Stabilization

Depending on the soil and project requirements, stabilization may involve cementitious materials, lime or other approved binders.

3. Ground Improvement

Other techniques may include replacement, grouting, stone columns, deep soil mixing or other engineered solutions.

4. Increase Foundation Area

A larger footing spreads the structural load over a greater area, reducing average contact pressure.

5. Use a Raft Foundation

A raft can distribute structural loads over a large area and may be considered where individual footings would become excessively large or where ground conditions make a raft advantageous.

6. Use Deep Foundations

Piles or other deep foundation systems may be considered when suitable supporting strata are located deeper below the surface.

Our article on building foundations discusses how soil conditions and structural loads influence foundation selection.

14. Soil Investigation Before Foundation Design

One of the biggest mistakes in foundation construction is treating a generic bearing-capacity value as though it applies automatically to every site.

A proper geotechnical investigation can help establish:

• soil profile;
• groundwater conditions;
• soil classification;
• strength parameters;
• density and stiffness;
• compressibility;
• potentially problematic layers;
• appropriate foundation options.

Depending on the project, investigation may include boreholes, trial pits, laboratory testing, Standard Penetration Testing, cone penetration testing or other appropriate methods.

SPT-based methods can also be used for estimating bearing capacity in appropriate granular-soil applications, but the selected correlations and groundwater corrections must match the method and site conditions.

Current geotechnical practice continues to emphasize investigation and the appropriate derivation of representative ground parameters before foundation design.

15. How Engineers Check a Foundation’s Load Bearing Capacity

A simplified foundation assessment can be thought of as a sequence:

1. Investigate the ground.
2. Determine representative soil parameters.
3. Calculate structural loads.
4. Select a preliminary foundation type.
5. Determine footing dimensions and depth.
6. Calculate bearing resistance/capacity.
7. Check the applied foundation pressure.
8. Check settlement.
9. Check sliding, overturning and overall stability where applicable.
10. Design the reinforced-concrete foundation itself.

This sequence is much safer than simply looking up a soil type and assigning it a generic load bearing capacity.

16. Bearing Pressure vs. Bearing Capacity

These two terms are easy to confuse.

Bearing pressure is the pressure actually applied to the soil by the foundation.

Bearing capacity is the resistance the soil can provide under the relevant design conditions.

The basic design concept is:

Applied foundation pressure ≤ permitted design bearing resistance

But that inequality alone is not a complete foundation design because settlement and other geotechnical limit states must also be checked.

17. Ultimate Bearing Capacity vs. Allowable Bearing Pressure

The important lesson is that a foundation should not be considered safe simply because its applied pressure is lower than a calculated ultimate bearing capacity.

18. Practical Example of Load Bearing Capacity

Suppose a square footing has dimensions of 2 m × 2 m.

The footing area is:

A = 2 × 2 = 4 m²

If the permitted design bearing pressure is 150 kPa:

Design ground load = 150 × 4 = 600 kN

This means the average permitted foundation pressure corresponds to approximately 600 kN over the 4 m² footing area under the simplified assumption.

In an actual design, the engineer must also consider the footing’s own weight, moments, eccentricity, load combinations and whether the 150 kPa value is gross or net.

19. What Happens When the Soil Bearing Capacity Is Too Low?

If investigation indicates inadequate load bearing capacity, several solutions may be considered.

• Increase the footing size.
• Increase foundation depth where appropriate.
• Improve or replace unsuitable soil.
• Use a raft foundation.
• Use piles or another deep foundation system.
• Reduce structural loads where possible.
• Modify the building layout or foundation arrangement.

The best solution depends on the actual ground profile, structural loads, groundwater and project economics.

For existing buildings experiencing foundation problems, underpinning may sometimes be considered. Read our guide on underpinning meaning and foundation strengthening for more information.

20. Soil Bearing Capacity and Foundation Selection

Soil conditions and structural loads work together when selecting a foundation system.

21. Common Mistakes When Estimating Soil Load Bearing Capacity

Mistake 1: Using a Generic Soil Value

A value copied from an internet table may not represent the actual soil at the site.

Mistake 2: Ignoring Groundwater

Groundwater can change effective stress and therefore influence bearing-capacity calculations.

Mistake 3: Checking Only Shear Failure

A foundation can satisfy a shear-capacity calculation while still experiencing unacceptable settlement.

Mistake 4: Mixing Gross and Net Values

Gross and net pressures must be clearly distinguished throughout the calculation.

Mistake 5: Using the Wrong Bearing-Capacity Factors

N_c, N_q and N_γ depend on the adopted theory. Shape and other correction factors may also be required.

Mistake 6: Ignoring Eccentricity

When loads are eccentric, the pressure distribution beneath a footing may no longer be uniform.

Mistake 7: Assuming Deeper Always Means Better

Increasing foundation depth can influence bearing resistance, but foundation depth must be selected based on soil profile, groundwater, structural requirements, excavation conditions and the applicable design criteria.

22. Frequently Asked Questions About Soil Bearing Capacity

What is soil bearing capacity?

Soil bearing capacity is the ability of the ground to resist the pressure transferred by a foundation under specified conditions. In engineering design, both ground strength and settlement need to be considered.

What is the formula for soil bearing capacity?

A commonly used simplified bearing-capacity equation for shallow foundations is:

q_u = c′N_c + γD_fN_q + ½γBN_γ

More complete equations introduce factors for footing shape, depth, load inclination, foundation-base inclination and ground slope.

What is load bearing capacity?

Load bearing capacity describes how much structural load the supporting ground can safely resist under the specified foundation and design conditions. Strictly speaking, engineers usually express soil bearing resistance as pressure, such as kPa, and then relate that pressure to the foundation area and structural load.

What is the difference between bearing capacity and bearing pressure?

Bearing pressure is the pressure applied by the foundation to the ground. Bearing capacity is the resistance available from the ground under the specified conditions.

What is ultimate bearing capacity?

Ultimate bearing capacity is the calculated resistance associated with the limiting ground failure condition in the adopted bearing-capacity model.

How is allowable bearing pressure calculated?

Under a traditional allowable-stress approach, an illustrative relationship is:

q_allow = q_u / FS

However, modern codes may use partial factors and limit-state procedures instead of one global factor of safety. The applicable design code should therefore control the calculation.

Does soil type determine bearing capacity?

Soil type is important, but it is not sufficient by itself. Strength, density, stress history, groundwater, foundation dimensions, embedment depth and loading conditions also affect the calculated bearing resistance and settlement.

Can water reduce soil bearing capacity?

Groundwater can affect effective stress and the unit weight used in bearing-capacity calculations. The effect depends on the groundwater position relative to the foundation and the adopted analysis.

Does a wider foundation increase load bearing capacity?

Increasing foundation width increases the area over which a structural load is distributed and can change the calculated bearing resistance. It can also reduce average applied pressure. However, the complete design must still satisfy both strength and settlement requirements.

How can the load bearing capacity of soil be increased?

Possible approaches include appropriate compaction, soil replacement, stabilization, ground improvement, increasing foundation area, using a raft foundation or transferring loads to deeper competent strata with deep foundations.

Is bearing capacity the same as settlement capacity?

No. Bearing capacity primarily addresses ground resistance, while settlement addresses deformation. Both can control foundation design.

What soil test is used to determine bearing capacity?

There is no single test suitable for every project. Depending on the ground and design requirements, engineers may use boreholes, laboratory strength tests, Standard Penetration Tests, cone penetration tests and other geotechnical investigations to establish suitable design parameters.

Can I use a soil bearing capacity value from the internet to design my house foundation?

It is not recommended. Generic values can be useful for education or preliminary discussion, but foundation design should be based on the actual site conditions and the requirements of the applicable building and geotechnical design standards.

23. Final Thoughts on Soil Bearing Capacity and Load Bearing Capacity

The soil bearing capacity formula is an important part of foundation engineering, but the formula itself is only one part of the design process.

A reliable assessment of load bearing capacity requires an understanding of:

• soil strength;
• soil layering;
• foundation width and shape;
• foundation depth;
• groundwater;
• structural loading;
• load eccentricity;
• the selected bearing-capacity theory;
• the applicable design code;
• settlement and other serviceability requirements.

The simplified examples in this article show how the basic equations work, but they should not be used as a substitute for a site-specific geotechnical and structural design.

For practical building projects, the foundation should be designed after the ground conditions and structural loads have been properly assessed.

For more information about foundation selection and how soil conditions influence building foundations, read Building Foundations: What You Should Know.

For existing structures where foundation capacity or settlement has become a concern, see our guide to underpinning in construction.

Technical references used for this update

• European Commission Joint Research Centre — Eurocode 7 guidance on shallow foundation design, bearing resistance and serviceability.
• Engineering LibreTexts — foundation engineering guidance on bearing-capacity equations, groundwater effects and net bearing capacity.
• FHWA — geotechnical guidance on settlement and foundation-soil interaction.
• Caltrans Geotechnical Manual — current guidance and resources for geotechnical investigation and foundation design.

Disclaimer: This article is provided for educational and general construction-information purposes. Soil and foundation design is site-specific. A qualified geotechnical and structural professional should verify the soil parameters, loads, foundation dimensions, groundwater conditions, settlement and applicable design requirements before construction.