Terzaghi Bearing Capacity Calculator
Calculate Terzaghi ultimate bearing capacity, gross allowable bearing capacity, net allowable bearing capacity, or required footing width for shallow foundation checks.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Select the result, footing type, shear mode, and unit setup.
Enter the known values
Use project-specific geotechnical values whenever available.
Visual Check
Connect the footing dimensions, embedment depth, surcharge, and bearing resistance.
Solution
Live result, bearing factors, checks, warnings, and full solution steps.
Quick checks
- Check—
Show solution steps See bearing factors, substitutions, assumptions, and result path
- Enter values to see the full solution steps and checks.
Source, Standards, and Assumptions
Calculation basis, constants, assumptions, and limitations.
- Assumptions will appear after a valid calculation.
On this page
Calculator Guide
How to Use the Terzaghi Bearing Capacity Calculator
The Terzaghi Bearing Capacity Calculator above estimates the ultimate and allowable soil bearing pressure for a shallow foundation using cohesion, friction angle, soil unit weight, footing geometry, embedment depth, surcharge, and factor of safety. It is best used for preliminary shear bearing capacity checks, not final foundation design.
Terzaghi’s method is one of the classic shallow foundation bearing capacity methods. It breaks bearing resistance into three parts: soil cohesion, surcharge at the footing base, and the weight/friction contribution of soil below the footing. In many real shallow foundation designs, settlement can control allowable pressure before shear bearing failure, so the calculator result should be treated as one check in a larger foundation review.
Quick Answer
For a strip footing, Terzaghi’s bearing capacity equation is \(q_{ult}=cN_c+qN_q+\frac{1}{2}\gamma BN_\gamma\). Gross allowable bearing capacity is usually calculated as \(q_{allow,gross}=q_{ult}/FS\), while net allowable capacity is commonly calculated as \(q_{allow,net}=(q_{ult}-q)/FS\). Use the calculator above to handle unit conversions, footing shape factors, local shear correction, and the full solution steps.
Do not rely on this simplified calculator when…
Do not use this calculator alone for final foundation design, construction approval, or code compliance. It does not check settlement, consolidation, bearing on layered soils, eccentric loading, inclined loading, uplift, sliding, overturning, groundwater changes, frost effects, seismic loading, nearby slopes, or site-specific geotechnical report requirements.
Inputs and Outputs Used by the Calculator
The calculator uses soil strength, soil weight, footing geometry, embedment depth, and factor of safety to estimate shallow foundation bearing pressure. Required inputs change slightly depending on whether you solve for ultimate capacity, allowable capacity, or required footing width.
| Type | Value | What It Means | Common Unit |
|---|---|---|---|
| Input | Cohesion, \(c\) | Soil shear strength intercept used in the bearing capacity equation. | kPa, psf, ksf |
| Input | Friction angle, \(\phi\) | Controls the bearing capacity factors \(N_c\), \(N_q\), and \(N_\gamma\). | degrees |
| Input | Soil unit weight, \(\gamma\) | Weight density of the soil used for surcharge and the unit-weight term. | kN/m³, pcf |
| Input | Footing width, \(B\) | Footing width for strip, square, and rectangular footings; diameter for circular footings. | m, ft |
| Input | Foundation depth, \(D_f\) | Depth from ground surface to footing base, often used to calculate surcharge \(q=\gamma D_f\). | m, ft |
| Input | Surcharge, \(q\) | Overburden pressure at the footing base. This is not the applied structural load. | kPa, psf, ksf |
| Input | Factor of safety, \(FS\) | Divides ultimate capacity to estimate allowable bearing capacity. | ratio |
| Output | Ultimate bearing capacity, \(q_{ult}\) | Estimated gross pressure at shear failure under Terzaghi assumptions. | kPa, psf, ksf |
| Output | Allowable bearing capacity | Ultimate capacity divided by factor of safety; may be shown as gross and net values. | kPa, psf, ksf |
| Output | Required footing width | Width required to meet a target allowable pressure when the width-dependent term controls. | m, ft |
If you are entering values from a geotechnical report, check whether the report gives allowable bearing pressure directly, undrained shear strength, effective stress parameters, groundwater-adjusted unit weight, or different values for short-term and long-term conditions.
Terzaghi Bearing Capacity Formula
Terzaghi’s formula estimates ultimate bearing capacity by adding the cohesion term, surcharge term, and soil unit-weight term. The exact expression changes with footing shape.
Strip Footing
This is the common base form for a long strip footing under centered vertical loading.
Square Footing
The square footing form modifies the cohesion and soil weight terms to account for shape.
Circular Footing
For circular footings, \(B\) is the footing diameter.
Rectangular Footing Shape Factors
A common simplified rectangular approach uses \(s_c=1+0.3(B/L)\) and \(s_\gamma=1-0.2(B/L)\), where \(L\) is footing length.
Bearing Capacity Factor Convention Used Here
Different references may use different \(N_\gamma\) expressions. If another bearing capacity calculator gives a different result, compare the exact bearing factor convention before assuming either result is wrong.
Local Shear Correction
When local shear correction is selected, the calculator reduces the strength parameters before calculating the bearing capacity factors.
Use local shear correction only when that is the intended analysis assumption. It can significantly reduce the calculated capacity.
Three practical insights
The \(cN_c\) term often dominates clay-like cases, the \(qN_q\) term increases with embedment depth, and the \(\frac{1}{2}\gamma BN_\gamma\) term is the only term that directly grows with footing width in the basic strip footing expression.
What the Variables Mean
Every variable should represent the same soil condition and unit system. Mixing total stress, effective stress, groundwater assumptions, or incompatible units can make the result look precise while being wrong.
| Symbol | Meaning | How to Enter It |
|---|---|---|
| \(q_{ult}\) | Gross ultimate bearing capacity at shear failure. | Output pressure, usually in kPa, psf, or ksf. |
| \(c\) | Cohesion or undrained shear strength parameter, depending on analysis basis. | Use report-recommended value. Do not mix drained and undrained parameters. |
| \(\phi\) | Soil friction angle. | Enter in degrees in the calculator. JavaScript calculations convert degrees to radians internally. |
| \(\gamma\) | Soil unit weight. | Use total or effective unit weight based on groundwater and analysis method. |
| \(B\) | Footing width or circular footing diameter. | Use the smaller plan dimension for rectangular footings. |
| \(L\) | Footing length for rectangular footing checks. | Enter length greater than or equal to \(B\). |
| \(D_f\) | Depth from ground surface to footing base. | Used to estimate surcharge when \(q=\gamma D_f\). |
| \(q\) | Surcharge at the footing base. | Use \(q=\gamma D_f\) or enter a manual surcharge if known. This is not the applied structural bearing pressure. |
| \(N_c,N_q,N_\gamma\) | Dimensionless bearing capacity factors. | Calculated from \(\phi\), with \(N_c=5.7\), \(N_q=1\), and \(N_\gamma=0\) commonly used for \(\phi=0^\circ\) in Terzaghi-style checks. |
| \(FS\) | Factor of safety. | Used to convert ultimate capacity into allowable capacity. |
How to Use the Calculator
Start by selecting the solve mode, then enter the soil parameters, footing type, footing dimensions, embedment depth, surcharge option, and factor of safety. The calculator above updates the required fields and output units based on the selected result.
Select the solve mode
Choose ultimate bearing capacity, gross allowable bearing capacity, or required footing width. Use required width only when you have a target allowable bearing pressure.
Choose footing type and shear mode
Select strip, square, circular, or rectangular footing. Use local shear correction only when that assumption matches the soil behavior you intend to model.
Enter soil and geometry values carefully
Enter \(c\), \(\phi\), \(\gamma\), \(B\), \(D_f\), and \(FS\). For rectangular footings, also enter \(L\). Confirm all unit selectors before trusting the result.
Review gross, net, and term contributions
Check whether the result is dominated by cohesion, surcharge, or the width-dependent unit-weight term. Large unexpected changes usually trace back to \(\phi\), unit weight, or unit conversion errors.
How to Interpret Bearing Capacity Results
A bearing capacity result is a pressure, not a complete foundation design. It should be compared against applied foundation pressure and reviewed with settlement, groundwater, soil profile, and load condition checks.
| Result Pattern | What It May Mean | What to Check Next |
|---|---|---|
| Low allowable capacity | Weak soil, low friction angle, shallow embedment, low cohesion, or conservative local shear correction. | Check soil parameters, groundwater, settlement, and whether a larger/deeper footing is appropriate. |
| Moderate allowable capacity | Typical preliminary result for many shallow foundation checks, depending on soil and footing geometry. | Compare against applied service pressure and settlement limits. |
| Very high capacity | May be caused by high \(\phi\), high cohesion, high unit weight, large footing width, or unit mistakes. | Verify input units and confirm values came from a geotechnical report. |
| Negative net allowable | Surcharge is large relative to calculated ultimate capacity. | Review depth, unit weight, and whether the analysis basis is appropriate. |
| Required width cannot be solved | The width-dependent term may not control, especially when \(N_\gamma=0\). | Check whether settlement, structural geometry, or applied load area controls instead. |
What to do with the result
Compare the allowable bearing capacity to the service bearing pressure from the footing load divided by footing area. Use \(q_{applied}=P/A\), where \(P\) is the applied service load and \(A\) is the footing contact area. If the applied pressure is close to the allowable capacity, do not stop at the Terzaghi check. Review settlement, eccentricity, groundwater, seasonal changes, and recommendations from the project geotechnical report.
Applied Bearing Pressure Check
For a rectangular footing, \(A=BL\). For a circular footing where \(B\) is diameter, \(A=\frac{\pi B^2}{4}\).
What changes the result most?
Friction angle usually has the largest nonlinear effect because it controls \(N_c\), \(N_q\), and \(N_\gamma\). Footing width affects only the \(\frac{1}{2}\gamma BN_\gamma\) term in the basic strip footing formula, while embedment depth increases surcharge through \(q=\gamma D_f\).
Practical sanity check
If changing \(\phi\) by only a few degrees causes a large jump in bearing capacity, that is expected mathematically but should trigger input verification. If a value looks extremely high, recheck whether you entered kPa vs psf, ksf vs kPa, m vs ft, or pcf vs kN/m³.
Input Quality Checklist
Terzaghi calculations are sensitive to input quality. Before using the result, confirm that each value represents the intended analysis condition.
Soil Strength Basis
Do not mix drained friction angle with an undrained cohesion value unless your geotechnical analysis specifically supports that combination.
Groundwater Condition
Use effective unit weight when groundwater reduces effective stress near the footing base.
Footing Geometry
For circular footings, \(B\) is diameter. For rectangular footings, \(B\) should be the smaller plan dimension and \(L\) the longer dimension.
Surcharge Definition
If using automatic surcharge, confirm that \(q=\gamma D_f\) is appropriate. Use manual surcharge when the overburden condition is known directly.
Factor of Safety
Use a factor of safety that matches the design basis, project requirements, and whether you are checking gross or net capacity.
Result Type
Do not confuse ultimate capacity with allowable capacity. Ultimate capacity is not the allowable working pressure.
Step-by-Step Worked Example
The example below calculates gross ultimate, gross allowable, and net allowable bearing capacity for a strip footing on granular soil using Terzaghi’s strip footing equation.
Factor convention used in this example
This example uses the same bearing factor convention as the calculator above: \(N_q=e^{\pi\tan\phi}\tan^2(45^\circ+\phi/2)\), \(N_c=(N_q-1)/\tan\phi\), and \(N_\gamma=2(N_q-1)\tan\phi\). Other references may use a different \(N_\gamma\), which can change the final value.
1. Calculate Surcharge
2. Use Bearing Factors for \(\phi=30^\circ\)
3. Substitute into Terzaghi’s Strip Footing Formula
4. Calculate Ultimate and Allowable Capacity
Result
Gross allowable bearing capacity: approximately 201 kPa. Net allowable bearing capacity: approximately 195 kPa.
Is the answer reasonable?
The result is plausible for a preliminary strip footing example on a frictional soil with \(\phi=30^\circ\), but it is only a shear bearing capacity estimate. The final footing design still needs settlement and project-specific geotechnical checks.
Engineering Diagram
A useful Terzaghi diagram shows the footing width \(B\), embedment depth \(D_f\), surcharge \(q\), bearing pressure, and simplified shear failure zones below the footing. The visual below is included directly in the page so it does not depend on separate image files.
Typical Reference Values and Reasonableness Ranges
Soil parameters vary widely by site, testing method, drainage condition, and groundwater level. Use these ranges only as broad reasonableness checks, not as design values.
| Parameter | Broad Typical Range | Important Caution |
|---|---|---|
| Friction angle, \(\phi\) | About \(25^\circ\) to \(40^\circ\) for many sands and granular soils | Density, gradation, stress level, and testing method matter. |
| Soil unit weight, \(\gamma\) | About 16 to 22 kN/m³ for many natural soils | Use effective unit weight below groundwater when appropriate. |
| Factor of safety, \(FS\) | Often around 2.5 to 3.0 for preliminary shear capacity checks | Project requirements and design method control the actual value. |
| \(\phi=0^\circ\) clay case | \(N_c=5.7\), \(N_q=1\), \(N_\gamma=0\) in common Terzaghi-style checks | Width may not increase the calculated shear capacity in the simplified equation. |
| Allowable bearing pressure | Highly site-specific | Often controlled by settlement before shear failure for many service conditions. |
Do not design from generic soil values
Generic soil ranges are useful for catching input errors, but they are not a substitute for borings, lab testing, in-situ testing, groundwater evaluation, and a project-specific geotechnical report.
Design Ranges and Practical Engineering Checks
A mathematically correct Terzaghi result is only one piece of shallow foundation design. In many real projects, settlement, differential settlement, groundwater, and constructability can control before shear bearing capacity does.
Service Pressure Check
Compare the allowable bearing capacity against the service load divided by footing area. Use the correct gross or net pressure basis.
Settlement Check
A footing can pass shear bearing capacity and still fail serviceability due to excessive total or differential settlement.
Geometry Check
Footing dimensions must also satisfy structural design, reinforcement layout, minimum dimensions, excavation limits, and constructability.
When width does not control
If \(\phi=0^\circ\), then \(N_\gamma=0\) in the common Terzaghi-style assumption. The \(\frac{1}{2}\gamma BN_\gamma\) term disappears, so increasing \(B\) may not increase calculated shear capacity in this simplified equation. A required-width result may also be reported as “not controlled” when the target allowable pressure is already satisfied by the cohesion and surcharge terms before the width-dependent soil-weight term is needed.
Unit Conversion Notes
Terzaghi’s formula is unit-consistent, which means pressure, unit weight, and length units must work together. The calculator handles conversions, but the input values still need to be entered under the correct unit labels.
| Quantity | Common Units | Conversion Reminder |
|---|---|---|
| Pressure | kPa, psf, ksf | \(1\,psf=0.0478803\,kPa\); \(1\,ksf=47.8803\,kPa\) |
| Length | m, ft | \(1\,ft=0.3048\,m\) |
| Unit weight | kN/m³, pcf | \(1\,pcf=0.157087\,kN/m^3\) |
| Friction angle | degrees | Use degrees in the calculator interface unless a formula explicitly requires radians internally. |
| Factor of safety | unitless | Do not enter as a percentage. Use 3, not 300%. |
Most common unit trap
The biggest mistake is switching from SI to U.S. customary units without converting the numeric values. For example, \(18\,kN/m^3\) is not \(18\,pcf\). It is about \(114.6\,pcf\).
Terzaghi vs Meyerhof, Hansen, Vesic, and Other Bearing Capacity Methods
Terzaghi’s method is a classic and useful preliminary method, but it is not the only bearing capacity approach. Other methods add correction factors for shape, depth, load inclination, eccentricity, ground slope, base inclination, and other real-world effects.
| Method or Check | Best For | Main Caution |
|---|---|---|
| Terzaghi | Classic shallow foundation checks, education, and preliminary strip/square/circular footing estimates. | Limited correction factors compared with more general methods. |
| Meyerhof | More general bearing capacity checks with additional shape, depth, and load inclination factors. | Requires more input assumptions than the basic Terzaghi form. |
| Hansen | Broader bearing capacity analysis with multiple correction factors. | More flexible, but also more sensitive to selected factors. |
| Vesic | Common modern bearing capacity comparisons and alternative factor conventions. | May produce different values from Terzaghi due to different \(N_\gamma\) treatment. |
| Settlement analysis | Serviceability check for total and differential settlement. | Can control even when bearing shear capacity is acceptable. |
If another bearing capacity calculator gives a different result, compare the \(N_\gamma\) equation, footing shape factors, depth factors, groundwater treatment, and whether the output is gross or net allowable capacity.
Common Mistakes That Cause Wrong Results
Bearing capacity calculations often fail because the formula is used correctly with the wrong inputs. The mistakes below are especially common when comparing textbook examples, calculator results, and geotechnical reports.
Common Mistakes
- Using ultimate bearing capacity as if it were allowable bearing capacity.
- Confusing gross allowable and net allowable bearing pressure.
- Entering \(B\) as length instead of the smaller footing dimension for rectangular footings.
- Using total unit weight when submerged/effective unit weight is required.
- Assuming a required width result is valid when \(N_\gamma=0\).
- Comparing results from different \(N_\gamma\) conventions without checking the factor equations.
Better Practice
- Use the same gross or net basis as the design load comparison.
- Verify \(c\), \(\phi\), and \(\gamma\) from a project-specific geotechnical source.
- Check whether the analysis is drained, undrained, total stress, or effective stress.
- Review the contribution of cohesion, surcharge, and unit weight terms.
- Run settlement checks before treating the footing design as complete.
- Document the bearing factor equations used for comparison and review.
Troubleshooting Unexpected Results
If the result seems wrong, check the input units and the result type first. Many suspicious outputs come from a gross/net mismatch, unit conversion error, or unrealistic friction angle.
| Problem | Likely Cause | Fix |
|---|---|---|
| Capacity is extremely high | High \(\phi\), wrong pressure unit, wrong unit weight, or using ksf/kPa incorrectly. | Verify unit selectors and compare soil parameters to the geotechnical report. |
| Capacity is very low | Low friction angle, low cohesion, local shear correction, shallow depth, or weak soil. | Check whether the selected shear mode and soil values are appropriate. |
| Required width returns no solution | The target may already be met or the equation may not depend on \(B\). | Review \(N_\gamma\), \(\phi\), and whether bearing capacity actually controls footing size. |
| Another calculator gives a different answer | Different bearing factors, shape factors, depth factors, \(N_\gamma\) equation, or gross/net convention. | Compare the exact formula and assumptions, not just the final number. |
| Net allowable is negative | Surcharge is large compared with calculated ultimate capacity. | Check \(D_f\), \(\gamma\), surcharge mode, and whether the model applies. |
Edge case competitors often miss
In a \(\phi=0^\circ\) case, \(N_\gamma=0\). Because the width-dependent term disappears, a “required width” solve mode may not have a meaningful bearing-capacity-controlled answer. This does not mean the footing can be zero width; it means another design condition controls.
Assumptions, Sources, and Limitations
This calculator is intended for educational use, preliminary checks, and transparent formula review. Terzaghi’s method is a simplified shallow foundation shear capacity model and should be used with engineering judgment.
Soil Assumption
Assumes a simplified soil profile and does not model layered soils, weak seams, variable groundwater, or spatial variability across the footing area.
Loading Assumption
Assumes centered vertical loading. Eccentric, inclined, uplift, moment, and combined loading require additional checks.
Geometry Assumption
Uses simplified footing shape treatment. Real foundations may require depth, inclination, slope, base tilt, and other correction factors.
Serviceability Limit
Does not check total settlement, differential settlement, consolidation, vibration, frost, expansive soil, or long-term movement.
Calculation basis and source note
This page uses Terzaghi-style shallow foundation bearing capacity equations and common bearing capacity factor relationships shown in the calculator solution steps. For broader shallow foundation design guidance, settlement checks, and project-specific design considerations, see the Federal Highway Administration reference Geotechnical Engineering Circular No. 6: Shallow Foundations.
Final design warning
Foundation design is safety-sensitive. Use this result only as a preliminary calculation or educational check. Final design should be based on a geotechnical report, applicable codes, structural loading, settlement analysis, groundwater review, construction conditions, and professional engineering judgment.
Glossary of Terms
These definitions help connect the calculator inputs to common geotechnical engineering terms.
Ultimate Bearing Capacity
The estimated gross foundation pressure at which a shear failure mechanism develops in the supporting soil.
Allowable Bearing Capacity
The bearing pressure used for service checks after applying a factor of safety to ultimate capacity.
Gross Bearing Pressure
Total pressure at the footing base, including the effect of overburden or surcharge depending on the comparison basis.
Net Bearing Pressure
Bearing pressure with the surcharge or overburden effect removed for comparison on a net basis.
Surcharge
Vertical overburden pressure at the footing base, often estimated as \(q=\gamma D_f\).
Bearing Capacity Factors
Dimensionless factors \(N_c\), \(N_q\), and \(N_\gamma\) that depend mainly on soil friction angle.
Local Shear
A bearing failure mode often associated with weaker or looser soils, sometimes modeled with reduced strength parameters.
Settlement
Vertical movement of a foundation under load. Settlement can control design even when shear bearing capacity is adequate.
Frequently Asked Questions
What does the Terzaghi Bearing Capacity Calculator calculate?
It estimates ultimate bearing capacity, gross allowable bearing capacity, net allowable bearing capacity, and, when bearing capacity controls, required footing width for shallow foundation checks.
What is the Terzaghi bearing capacity formula?
For a strip footing, the common Terzaghi formula is \(q_{ult}=cN_c+qN_q+\frac{1}{2}\gamma BN_\gamma\), where \(c\) is cohesion, \(q\) is surcharge, \(\gamma\) is soil unit weight, \(B\) is footing width, and \(N_c\), \(N_q\), and \(N_\gamma\) are bearing capacity factors.
What is the difference between gross and net allowable bearing capacity?
Gross allowable bearing capacity is \(q_{ult}/FS\). Net allowable bearing capacity removes surcharge before applying the factor of safety and is commonly written as \((q_{ult}-q)/FS\). Use the same gross or net basis as your load comparison.
Why can required footing width fail to solve when \(\phi=0^\circ\)?
When \(\phi=0^\circ\), \(N_\gamma\) is commonly taken as zero. That removes the width-dependent \(\frac{1}{2}\gamma BN_\gamma\) term, so the simplified Terzaghi shear capacity may not increase with width.
Why does another calculator give a different bearing capacity?
Different calculators may use different \(N_\gamma\) equations, shape factors, depth factors, groundwater assumptions, local shear corrections, or gross/net output conventions. Compare the full formula and assumptions, not only the final number.
Can this calculator be used for final foundation design?
No. It is useful for education and preliminary checks, but final design should also evaluate settlement, groundwater, soil layering, eccentricity, inclined loads, slopes, seismic conditions, construction limits, and applicable geotechnical report recommendations.