# Bearing Capacity Calculator (Terzaghi) Calculate the Terzaghi ultimate bearing capacity of a shallow foundation: q_ult = c·Nc·sc + q·Nq·sq + 0.5·γ·B·Nγ·sγ. Computes Nc/Nq/Nγ and shape factors automatically; supports strip, square, and circular footings. Result in kPa. > Canonical page: https://elysiatools.com/en/tools/bearing-capacity-calculator - **Category:** Math & Numbers - **Keywords:** bearing capacity, Terzaghi, shallow foundation, Nc Nq Nγ, ultimate bearing capacity, geotechnical, foundation design, soil mechanics, civil engineering ## 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. ## Inputs - **Foundation Shape** (select) - **Cohesion c (kPa)** (number): Soil cohesion (undrained or effective). Use 0 for cohesionless soil. - **Friction Angle φ (°)** (number): 0 ≤ φ < 90. Use 0 for undrained clay (φ=0 analysis). - **Soil Unit Weight γ (kN/m³)** (number): e.g. 18 - **Foundation Width B (m)** (number): Foundation width (or diameter for circular). - **Embedment Depth Df (m)** (number): Depth of foundation base below ground surface. - **Decimal Places** (number) ## 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 - Select the foundation shape (strip, square, or circular) and input the soil parameters including cohesion, friction angle, and unit weight. - Enter the physical dimensions of the foundation, specifically the width (or diameter) and the embedment depth. - The calculator automatically computes the bearing capacity factors (Nc, Nq, Nγ) and shape factors (sc, sq, sγ) based on the friction angle and foundation geometry. - The 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. ## Frequently asked questions ### 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? 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