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Bearing Capacity Calculator - Terzaghi Meyerhof

Free Bearing capacity terzaghi meyerhof Calculator for soil & sediment mechanics. Enter variables to compute results with formulas and detailed steps.

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Earth Science & Geology

Bearing Capacity Calculator (terzaghi Meyerhof)

Calculate the ultimate and allowable bearing capacity of shallow foundations using Terzaghi and Meyerhof methods with soil parameters.

Last updated: December 2025Reviewed by NovaCalculator Mathematics Team

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Terzaghi Method

Nc = 20.72, Nq = 10.66, Ng = 10.88

898.06 kPa

Ultimate Bearing Capacity

299.35 kPa

Allowable (FOS = 3)

Meyerhof Method

Nc = 20.72, Nq = 10.66, Ng = 6.77

824.07 kPa

Ultimate Bearing Capacity

274.69 kPa

Allowable (FOS = 3)

Understand the Math

Formula

q_u = c * Nc + gamma * Df * Nq + 0.5 * gamma * B * Ng

This Bearing Capacity Calculator (Terzaghi & Meyerhof) computes results from your provided inputs using the calculator's underlying model.

Last reviewed: December 2025

Expert Insights

Background & Theory

The Bearing Capacity Calculator (terzaghi Meyerhof) applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) โˆ’ 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0โ€“12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1โ€“10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5โ€“7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 ร— exp(โˆ’Mgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.

History

The history behind the Bearing Capacity Calculator (terzaghi Meyerhof) traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity โ€” foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.

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Frequently Asked Questions

The Terzaghi bearing capacity equation estimates the ultimate bearing capacity of a shallow strip foundation as q_u = c * Nc + gamma * Df * Nq + 0.5 * gamma * B * Ng. Here c is soil cohesion, gamma is soil unit weight, Df is foundation depth, B is foundation width, and Nc, Nq, and Ng are bearing capacity factors that depend on the internal friction angle. This classical equation assumes a general shear failure mode in the soil beneath the footing.
The Meyerhof method extends the Terzaghi approach by including shape, depth, and inclination correction factors, making it more versatile for different foundation geometries and loading conditions. Meyerhof also uses a different set of bearing capacity factors derived from a more rigorous slip-line analysis. In practice, Meyerhof tends to give slightly higher bearing capacities for deeper foundations because the depth factor accounts for the shear strength of soil above the footing base.
A factor of safety of 3.0 is commonly used for bearing capacity design in most building codes and geotechnical standards. This means the allowable bearing pressure is one-third of the ultimate bearing capacity. For temporary structures or well-characterized soil conditions, a factor of safety of 2.0 to 2.5 may be acceptable, while critical structures may require higher values. The factor of safety accounts for soil variability, load uncertainties, and simplified assumptions in the bearing capacity theory.
Bearing capacity factors Nc, Nq, and Ng are dimensionless coefficients that depend on the internal friction angle of the soil. Nc represents the contribution of cohesion to bearing capacity, Nq represents the contribution of the overburden pressure (surcharge), and Ng represents the contribution of the soil self-weight below the foundation. As the friction angle increases, all three factors increase exponentially, reflecting the greater shear strength of more frictional soils.
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings.Reviewed by: NovaCalculator Mathematics Team โ€” Verified against standard mathematical and scientific references. Last reviewed: December 2025. ยฉ 2024โ€“2026 NovaCalculator.

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Formula

q_u = c * Nc + gamma * Df * Nq + 0.5 * gamma * B * Ng

This Bearing Capacity Calculator (Terzaghi & Meyerhof) computes results from your provided inputs using the calculator's underlying model.

Frequently Asked Questions

What is the Terzaghi bearing capacity equation?

The Terzaghi bearing capacity equation estimates the ultimate bearing capacity of a shallow strip foundation as q_u = c * Nc + gamma * Df * Nq + 0.5 * gamma * B * Ng. Here c is soil cohesion, gamma is soil unit weight, Df is foundation depth, B is foundation width, and Nc, Nq, and Ng are bearing capacity factors that depend on the internal friction angle. This classical equation assumes a general shear failure mode in the soil beneath the footing.

How does the Meyerhof method differ from Terzaghi?

The Meyerhof method extends the Terzaghi approach by including shape, depth, and inclination correction factors, making it more versatile for different foundation geometries and loading conditions. Meyerhof also uses a different set of bearing capacity factors derived from a more rigorous slip-line analysis. In practice, Meyerhof tends to give slightly higher bearing capacities for deeper foundations because the depth factor accounts for the shear strength of soil above the footing base.

What factor of safety should I use for bearing capacity?

A factor of safety of 3.0 is commonly used for bearing capacity design in most building codes and geotechnical standards. This means the allowable bearing pressure is one-third of the ultimate bearing capacity. For temporary structures or well-characterized soil conditions, a factor of safety of 2.0 to 2.5 may be acceptable, while critical structures may require higher values. The factor of safety accounts for soil variability, load uncertainties, and simplified assumptions in the bearing capacity theory.

What are bearing capacity factors Nc, Nq, and Ng?

Bearing capacity factors Nc, Nq, and Ng are dimensionless coefficients that depend on the internal friction angle of the soil. Nc represents the contribution of cohesion to bearing capacity, Nq represents the contribution of the overburden pressure (surcharge), and Ng represents the contribution of the soil self-weight below the foundation. As the friction angle increases, all three factors increase exponentially, reflecting the greater shear strength of more frictional soils.

How accurate are the results from Bearing Capacity Calculator - Terzaghi Meyerhof?

All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.

Is my data stored or sent to a server?

No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.

References

Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy