Bearing Capacity Calculator (Terzaghi)

Bearing Capacity Calculator (Terzaghi) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: select, number
Output type: json
Sample coverage: 4
API ready: Yes

Overview

The Terzaghi Bearing Capacity Calculator computes the ultimate bearing capacity of shallow foundations using Terzaghi's classic formulation. By entering the foundation shape, soil cohesion, friction angle, unit weight, foundation width, and embedment depth, you can instantly determine the bearing capacity factors, shape factors, and the final ultimate bearing capacity in kPa.

When to use

Designing shallow foundations such as strip, square, or circular footings in geotechnical engineering projects.
Verifying soil bearing capacity calculations during preliminary foundation design and feasibility studies.
Validating manual Terzaghi equation calculations for soil mechanics coursework or professional reports.

How it works

1Select the foundation shape (strip, square, or circular) and input the soil parameters including cohesion, friction angle, and unit weight.
2Enter the physical dimensions of the foundation, specifically the width (or diameter) and the embedment depth.
3The calculator automatically computes the bearing capacity factors (Nc, Nq, Nγ) and shape factors (sc, sq, sγ) based on the friction angle and foundation geometry.
4The tool applies the Terzaghi equation to calculate the cohesion, surcharge, and self-weight terms, summing them to output the ultimate bearing capacity in kPa.

Use cases

Calculating the ultimate bearing capacity of a continuous strip footing for a retaining wall.
Determining the allowable bearing capacity of a square column footing by applying a factor of safety to the ultimate capacity.
Analyzing the bearing capacity of a circular silo foundation resting on cohesive clay soil.

Examples

1. Strip Footing on Cohesionless Sand

Geotechnical Engineer

Background

An engineer needs to determine the ultimate bearing capacity for a long concrete retaining wall foundation resting on dry sand.

Problem

The sand has no cohesion (c = 0 kPa), a friction angle of 30°, and a unit weight of 18 kN/m³. The footing is 2 meters wide and buried 1 meter deep.

How to use

Select 'Strip' as the foundation shape, set cohesion to 0, friction angle to 30, unit weight to 18, width to 2, and embedment depth to 1.

{
  "shape": "strip",
  "c": 0,
  "phi": 30,
  "gamma": 18,
  "B": 2,
  "Df": 1,
  "decimalPlaces": 4
}

Outcome

The calculator outputs an ultimate bearing capacity of approximately 613.24 kPa, showing the individual surcharge term (331.22 kPa) and self-weight term (282.02 kPa).

2. Square Column Footing on Clayey Soil

Structural Designer

Background

A designer is sizing a square pad footing for a building column resting on a clayey sand layer.

Problem

The soil has a cohesion of 20 kPa, a friction angle of 25°, and a unit weight of 19 kN/m³. The footing is 2 meters wide and embedded 1.5 meters deep.

FAQ

What foundation shapes are supported by this calculator?

The calculator supports strip (continuous), square, and circular shallow footings.

How does the calculator handle cohesionless soils?

For cohesionless soils, such as clean sands, set the cohesion value (c) to 0 kPa.

What formula is used to calculate the bearing capacity factors?

It uses Terzaghi's equations where Nq = e^(π·tanφ)·tan²(45 + φ/2), Nc = (Nq - 1)·cotφ, and Nγ = (Nq - 1)·tan(1.4φ) or equivalent standard approximations.

What unit system does this calculator use?

It uses metric units: kPa for cohesion and bearing capacity, kN/m³ for unit weight, and meters for dimensions.

Can I use this calculator for deep foundations?

No, this calculator is specifically designed for shallow foundations where the embedment depth is typically less than or equal to the foundation width.

{
  "shape": "square",
  "c": 20,
  "phi": 25,
  "gamma": 19,
  "B": 2,
  "Df": 1.5,
  "decimalPlaces": 4
}

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Examples that match this tool

Continue with connected tools and hubs

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Strip Footing on Cohesionless Sand

2. Square Column Footing on Clayey Soil

FAQ

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