Terzaghi Bearing Capacity Calculator

Estimate ultimate and allowable soil bearing capacity for shallow foundations using Terzaghi’s equation, footing type, and soil parameters.

Configuration

Choose what you want to solve for and how the footing is shaped in plan.

Soil Properties (Effective)

Use effective stress parameters at foundation level for drained conditions.

Footing Geometry & Safety

Define footing depth and width, plus the factor of safety for allowable capacity. For circular footings, the width \(B\) is taken as the footing diameter; for square footings it is the side length.

Results Summary

The main result is shown below, with quick stats for both ultimate and allowable bearing capacities.

Practical Geotechnical Guide

Terzhagi’s Bearing Capacity Calculator

Learn how to use Terzaghi-style bearing capacity equations to size shallow foundations safely. This guide walks through inputs, design assumptions, typical soil parameters, and worked examples so you can interpret the calculator’s results with confidence.

8–12 min read Shallow foundations · Ultimate & allowable capacity

Quick Start: Using the Bearing Capacity Calculator Safely

This page assumes you are using a Terzaghi-style bearing capacity calculator for shallow foundations (footings close to the ground surface) under vertical, concentric loading. The calculator is not meant for deep foundations, heavily inclined loading, or seismic liquefaction assessment.

  1. 1 Choose the footing type. Select strip, square, or circular footing to match your actual layout. Shape factors and bearing capacity factors change with this selection, so the calculator equations and outputs will update.
  2. 2 Enter soil parameters. Provide: cohesion \(c\) (or undrained strength \(c_u\)), friction angle \(\varphi\), and unit weight \(\gamma\). Use values from a geotechnical report whenever possible.
  3. 3 Define footing geometry. Input footing width/diameter \(B\), length \(L\) (for strip/rectangular), and embedment depth \(D_f\). Keep units consistent with the calculator’s dropdowns (m, ft, kN/m³, pcf, etc.).
  4. 4 Select capacity type. Most workflows start by solving for ultimate bearing capacity \(q_u\) and then an allowable bearing capacity \(q_\text{allow}\) using a factor of safety \(FS\): \[ q_\text{allow} = \frac{q_u}{FS} \]
  5. 5 Apply a realistic factor of safety. Typical values are \(FS = 2.5 \text{–} 3.0\) for serviceability-based designs, but always follow your code and geotechnical recommendations.
  6. 6 Compare demand vs. capacity. Use the calculator’s allowable bearing capacity to check your applied contact stress: \[ \sigma_\text{applied} = \frac{P}{B \times L} \] Ensure \(\sigma_\text{applied} \leq q_\text{allow}\).
  7. 7 Perform sanity checks. Compare with values from the geotechnical report, similar projects, and code minimums. If the calculator result is far larger or smaller than expectations, revisit the inputs.

Tip: If you have both drained parameters \((c’, \varphi, \gamma’)\) and undrained strength \(c_u\), run both scenarios and adopt the more conservative design.

Warning: Terzaghi’s classical equations assume shallow footings on homogeneous soil, without strong layering, uplift, or seismic liquefaction. For complex profiles, always defer to a geotechnical engineer.

Choosing Your Bearing Capacity Method

There are many ways to estimate bearing capacity. The calculator on this page is built around Terzaghi-style equations, which remain a common starting point in practice. It also lets you move between ultimate and allowable capacities and choose different footing shapes.

Method A — Terzaghi Strip Footing (Classic)

The original Terzaghi equation for a strip footing on a homogeneous soil under vertical load is:

\[ q_u = c N_c + \gamma D_f N_q + \tfrac{1}{2} \gamma B N_\gamma \]
  • Simple, widely taught, easy to implement in a calculator.
  • Good for preliminary sizing and baseline checks.
  • Works well when footings are long compared to width (strip footing assumption).
  • Strictly valid for strip geometry; square/circular cases need shape factors.
  • Assumes vertical, centric loading on level ground without strong layering.

Method B — Shape-Adjusted Footings (Square & Circular)

For square and circular footings, the calculator applies shape factors \((s_c, s_q, s_\gamma)\) to Terzaghi’s base equation:

\[ q_u = c N_c s_c + \gamma D_f N_q s_q + \tfrac{1}{2} \gamma B N_\gamma s_\gamma \]
  • Reflects higher capacity for more compact footing shapes.
  • Common in many textbooks and design guides.
  • Calculator can switch shape factors automatically when you change footing type.
  • Shape factors vary slightly between references and codes.
  • Still assumes shallow footing and vertical loading.

Method C — Allowable Capacity with Safety Factor

Once the calculator finds \(q_u\), you can convert it to an allowable bearing capacity:

\[ q_\text{allow} = \frac{q_u}{FS} \]
  • Directly usable in working-stress design checks.
  • Easy to compare with code or report-provided allowable values.
  • Does not by itself address settlement limits.
  • Choice of \(FS\) must follow geotechnical recommendations and code.

Rule of thumb: Use the strip footing option for long wall footings, the square option for isolated column pads, and the circular option for pedestal or tank supports, then compare capacities across these shapes if geometry could change.

What Moves the Bearing Capacity Number

Terzaghi’s equation condenses a complex failure mechanism into a few key variables. The calculator exposes these variables so you can see which levers matter most and how sensitive your footing is to each.

Friction angle \(\varphi\)

In granular soils, \(\varphi\) has a huge impact because it controls the bearing capacity factors \(N_c\), \(N_q\), and \(N_\gamma\). A small increase in \(\varphi\) (e.g., 30° to 34°) can significantly increase \(q_u\).

Cohesion or undrained strength \(c\)

In cohesive soils, especially under undrained loading, the cohesion term \(c N_c\) can dominate. For purely cohesive clays with \(\varphi \approx 0^\circ\), Terzaghi’s equation simplifies and \(c\) becomes the main driver.

Footing width \(B\)

A wider footing mobilizes more soil and increases the contribution of the \(\tfrac{1}{2}\gamma B N_\gamma\) term. This is why bearing capacity often rises nonlinearly as you increase footing size.

Embedment depth \(D_f\)

Greater depth generally increases confinement and the overburden term \(\gamma D_f N_q\). However, deeper footings also interact more with groundwater and underlying layers.

Unit weight \(\gamma\) and groundwater

The effective unit weight (especially above and below groundwater level) affects both overburden and surcharge. The calculator assumes an average \(\gamma\); for layered soils, use a geotechnical report.

Factor of safety \(FS\)

Increasing \(FS\) reduces \(q_\text{allow}\), sometimes more effectively than tweaking geometry. Use the calculator’s quick stats to explore how different \(FS\) values shift your allowable capacity.

Worked Examples With Terzaghi-Style Equations

The examples below mirror what the calculator is doing behind the scenes. Values are illustrative; always use site-specific soil parameters for actual design.

Example 1 — Strip Footing in Sand (Drained)

  • Footing type: Strip footing (long wall)
  • Width: \(B = 2.0\ \text{m}\)
  • Depth: \(D_f = 1.5\ \text{m}\)
  • Soil: Medium dense sand, \(\varphi = 30^\circ\), \(c \approx 0\)
  • Unit weight: \(\gamma = 18\ \text{kN/m}^3\)
  • Factor of safety: \(FS = 3.0\)
1
Get bearing capacity factors. For \(\varphi = 30^\circ\), a typical set is \(N_q \approx 18.4\), \(N_c \approx 30.1\), \(N_\gamma \approx 22.4\). For clean sand, we often take \(c \approx 0\).
2
Compute ultimate bearing capacity. For a strip footing:
Equation
\[ q_u = c N_c + \gamma D_f N_q + \tfrac{1}{2}\gamma B N_\gamma \] \[ q_u \approx 0 + 18 \times 1.5 \times 18.4 + \tfrac{1}{2} \times 18 \times 2.0 \times 22.4 \] \[ q_u \approx 900\ \text{kPa} \ (\text{rounded}) \]
3
Convert to allowable capacity.
Equation
\[ q_\text{allow} = \frac{q_u}{FS} = \frac{900}{3.0} \approx 300\ \text{kPa} \]
4
Check against applied stress. If the wall load is \(P = 600\ \text{kN/m}\), then \(\sigma_\text{applied} = P / B = 600 / 2.0 = 300\ \text{kPa}\). This just equals \(q_\text{allow}\), so increasing \(B\) or \(FS\) may be prudent.

Example 2 — Square Footing in Clay (Undrained)

  • Footing type: Square footing
  • Width: \(B = 1.5\ \text{m}\)
  • Depth: \(D_f = 1.2\ \text{m}\)
  • Soil: Saturated clay, undrained strength \(c_u = 60\ \text{kPa}\)
  • Unit weight: \(\gamma = 18\ \text{kN/m}^3\)
  • Friction angle: \(\varphi \approx 0^\circ\)
  • Factor of safety: \(FS = 3.0\)
1
Select clay bearing capacity factors. For \(\varphi = 0^\circ\), one common choice is \(N_c \approx 5.14\), \(N_q \approx 1.0\), \(N_\gamma \approx 0\). For a square footing, we may apply a shape factor \(s_c \approx 1.3\).
2
Compute ultimate capacity. Neglecting the \(\gamma\)–\(N_\gamma\) term for \(\varphi = 0^\circ\):
Equation
\[ q_u \approx c_u N_c s_c + \gamma D_f N_q \] \[ q_u \approx 60 \times 5.14 \times 1.3 + 18 \times 1.2 \times 1.0 \] \[ q_u \approx 400\ \text{kPa} \ (\text{order of magnitude}) \]
3
Compute allowable capacity.
Equation
\[ q_\text{allow} = \frac{q_u}{FS} \approx \frac{400}{3.0} \approx 130\ \text{kPa} \]
4
Check plan size and settlements. If your column load is \(P = 2500\ \text{kN}\), the applied stress is \(P / B^2 = 2500 / 1.5^2 \approx 1110\ \text{kPa}\), which is far above the allowable capacity. The calculator will show that you must either increase \(B\) substantially or change the foundation system.

In real projects, settlement often governs clay footings before bearing failure does, so always pair these calculations with settlement checks from your geotechnical report.

Common Layouts & Variations for Shallow Footings

The same Terzaghi-style calculator can support a variety of footing layouts. The table below shows how the assumptions shift with common configurations.

ConfigurationTypical UseKey AssumptionsPros / Cons
Strip footingWall foundations, long machinery basesLength \( \gg B \); plane strain; Terzaghi strip factors Pros: Simple, continuous support.
Cons: Sensitive to differential settlements along the wall.
Square footingIsolated column pads, building columnsPlan aspect ratio near 1:1, shape factors \(s_c, s_q, s_\gamma\) applied Pros: Compact, efficient use of plan area.
Cons: Punching and reinforcement details can govern.
Circular footingTanks, silos, pedestalsAxisymmetric loading, circular plan with appropriate shape factors Pros: Uniform stress distribution under concentric loads.
Cons: Formwork and reinforcement can be more complex.
Combined footing / strapClosely spaced columns, property line constraintsNot strictly Terzaghi; 2D load sharing and stiffness effects Pros: Helps share loads where isolated pads would overlap.
Cons: Requires more advanced analysis than a single footing.
  • Check that the chosen footing type matches the actual plan geometry.
  • Verify that the load is approximately concentric; eccentricity reduces capacity.
  • Make sure the ground surface is reasonably level around the footing.
  • Review whether nearby footings might cause overlapping failure mechanisms.
  • Confirm that the soil profile is roughly uniform over the failure zone depth.
  • Use reduced effective unit weights if groundwater is close to the footing base.

Specs, Logistics & Sanity Checks Before Finalizing Design

While there is nothing to “buy” in the usual sense of a calculator, there are several design-specification and field-logistics checks you should make before relying on a single bearing capacity number.

Design Inputs & Specs

Before you lock in a footing size from the calculator, confirm the following design inputs against a geotechnical report or lab data:

  • Friction angle \(\varphi\) and cohesion \(c\) are taken from tests, not generic tables.
  • Unit weights are effective values, accounting for saturation and groundwater.
  • Design values reflect the governing load combination (dead, live, wind, seismic).
  • Factors of safety or resistance factors match the relevant design code.

Construction & Field Conditions

During construction, actual conditions often deviate from assumptions. Use the calculator to explore the sensitivity of your footing to realistic variations:

  • What if the excavation goes slightly deeper or shallower than designed?
  • What if the field moisture content is higher, reducing shear strength?
  • What if the contractor widens the footing by 100–200 mm for constructability?

If small changes trigger large swings in capacity, you may need a more robust footing or tighter construction controls.

Sanity Checks Before Sign-Off

As a final pass, use the calculator as a quick “what-if” engine:

  • Compare calculated \(q_\text{allow}\) to the allowable value in the geotechnical report.
  • Check bearing capacity at multiple depths if the soil profile is layered.
  • Compare with historic designs on similar sites or local rules of thumb.
  • Run both drained and undrained cases where applicable and adopt the worst case.

Important: A bearing capacity calculator supports, but does not replace, the judgment of a licensed geotechnical engineer. Always treat results as one input to a broader design decision that includes settlement, stability, and constructability.

Frequently Asked Questions

What is Terzaghi's bearing capacity equation used for?
Terzaghi's bearing capacity equation estimates the ultimate bearing capacity of a shallow foundation under vertical, centric loading. It provides a theoretical upper bound on how much stress the soil can carry before a shear failure mechanism forms beneath the footing. Designers then apply a factor of safety to obtain an allowable bearing capacity for service-level checks.
What is the difference between ultimate and allowable bearing capacity?
Ultimate bearing capacity \(q_u\) is the theoretical maximum stress that would trigger a shear failure. Allowable bearing capacity \(q_\text{allow}\) is the safe working value used in design, typically defined as: \[ q_\text{allow} = \frac{q_u}{FS} \] where \(FS\) is a factor of safety. The calculator can report both values so you can compare them to applied stresses.
Can I use this calculator for deep foundations or piles?
No. Terzaghi's shallow bearing capacity equation is not appropriate for piles, drilled shafts, or other deep foundations. Those systems rely on different failure mechanisms (shaft friction, end bearing at depth, group effects) and must be designed using methods specific to deep foundations.
How should I choose the bearing capacity factors Nc, Nq, and Nγ?
Bearing capacity factors \(N_c\), \(N_q\), and \(N_\gamma\) depend primarily on the soil friction angle \(\varphi\). The calculator uses standard relationships from classical bearing capacity theory, but in practice you should follow the values recommended in your geotechnical report. If the report provides specific factors or allowable bearing pressures, those override generic textbook values.
Does groundwater affect Terzaghi bearing capacity calculations?
Yes. Groundwater reduces effective unit weight and can significantly lower both shear strength and bearing capacity. If the water table lies near the footing base, the effective unit weight \(\gamma'\) should be used in the Terzaghi equation. When in doubt, consult the geotechnical report for guidance on how to account for groundwater.
Is bearing capacity or settlement usually more critical?
For many real projects—especially on clays or compressible soils—settlement limits control the design before bearing failure becomes critical. Terzaghi's equation is excellent for checking ultimate capacity, but you should always pair it with settlement estimates and code-prescribed serviceability criteria.
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