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Grain Size Uniformity Coefficient Calculator

Free Grain size uniformity coefficient Calculator for soil & sediment mechanics. Enter variables to compute results with formulas and detailed steps.

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Earth Science & Geology

Grain Size Uniformity Coefficient Calculator

Calculate coefficient of uniformity Cu, coefficient of curvature Cc, and USCS soil classification from grain size distribution parameters D10, D30, D50, and D60.

Last updated: December 2025Reviewed by NovaCalculator Mathematics Team

Calculator

Adjust values & calculate

8.00

Uniformity Coefficient (Cu)

0.98

Curvature Coefficient (Cc)

2.83

Sorting Coefficient (So)

Gradation

Poorly Graded

USCS Classification: SP

Soil Description

Medium Sand

Hazen k estimate: 2.2500 cm/s

Grain Size Summary

0.15 mm

D10

0.42 mm

D30

0.85 mm

D50

1.2 mm

D60

Understand the Math

Formula

Cu = D60 / D10; Cc = (D30)^2 / (D10 * D60)

This Grain Size Uniformity Coefficient Calculator computes results from your provided inputs using the calculator's underlying model.

Last reviewed: December 2025

Expert Insights

Background & Theory

The Grain Size Uniformity Coefficient Calculator 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 Grain Size Uniformity Coefficient Calculator 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 coefficient of uniformity Cu is the ratio of D60 to D10, where D60 is the grain diameter at which 60% of the soil by weight is finer, and D10 is the diameter at which 10% is finer. Cu measures the range of grain sizes present in the soil. A Cu value close to 1 indicates a uniform soil with particles of similar size. For sands, Cu greater than or equal to 6 indicates well-graded soil, while for gravels the threshold is Cu greater than or equal to 4. Well-graded soils generally have better engineering properties because smaller particles fill voids between larger ones.
The coefficient of curvature Cc, also called the coefficient of gradation, is calculated as (D30)^2 / (D10 * D60). It measures the shape of the grain size distribution curve between D10 and D60. For a soil to be classified as well-graded, Cc must fall between 1 and 3 in addition to meeting the Cu criterion. A Cc outside this range indicates a gap-graded or skip-graded soil that is missing certain intermediate grain sizes, even if Cu is high. Both Cu and Cc must satisfy their criteria simultaneously for well-graded classification.
Grain size analysis uses two complementary methods. For particles larger than 0.075 mm (retained on No. 200 sieve), mechanical sieve analysis is performed by passing soil through a stack of sieves with progressively smaller openings and weighing the retained material on each sieve. For particles finer than 0.075 mm, hydrometer analysis uses Stokes law to determine particle sizes from their settling velocity in a water suspension. The combined results produce the grain size distribution curve, from which D10, D30, D50, and D60 values are read.
Grain size distribution affects virtually every engineering property of coarse-grained soils. Well-graded soils achieve higher compacted densities, have greater shear strength, lower permeability, and less settlement under load compared to uniformly graded soils. The D10 size (effective size) is used to estimate hydraulic conductivity through correlations like the Hazen formula. Grain size distribution is the primary basis for USCS soil classification and directly influences filter design criteria for earth dams, drainage systems, and erosion control.
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

Cu = D60 / D10; Cc = (D30)^2 / (D10 * D60)

This Grain Size Uniformity Coefficient Calculator computes results from your provided inputs using the calculator's underlying model.

Frequently Asked Questions

What is the coefficient of uniformity (Cu)?

The coefficient of uniformity Cu is the ratio of D60 to D10, where D60 is the grain diameter at which 60% of the soil by weight is finer, and D10 is the diameter at which 10% is finer. Cu measures the range of grain sizes present in the soil. A Cu value close to 1 indicates a uniform soil with particles of similar size. For sands, Cu greater than or equal to 6 indicates well-graded soil, while for gravels the threshold is Cu greater than or equal to 4. Well-graded soils generally have better engineering properties because smaller particles fill voids between larger ones.

What is the coefficient of curvature (Cc)?

The coefficient of curvature Cc, also called the coefficient of gradation, is calculated as (D30)^2 / (D10 * D60). It measures the shape of the grain size distribution curve between D10 and D60. For a soil to be classified as well-graded, Cc must fall between 1 and 3 in addition to meeting the Cu criterion. A Cc outside this range indicates a gap-graded or skip-graded soil that is missing certain intermediate grain sizes, even if Cu is high. Both Cu and Cc must satisfy their criteria simultaneously for well-graded classification.

How is grain size analysis performed?

Grain size analysis uses two complementary methods. For particles larger than 0.075 mm (retained on No. 200 sieve), mechanical sieve analysis is performed by passing soil through a stack of sieves with progressively smaller openings and weighing the retained material on each sieve. For particles finer than 0.075 mm, hydrometer analysis uses Stokes law to determine particle sizes from their settling velocity in a water suspension. The combined results produce the grain size distribution curve, from which D10, D30, D50, and D60 values are read.

Why does grain size distribution matter in geotechnical engineering?

Grain size distribution affects virtually every engineering property of coarse-grained soils. Well-graded soils achieve higher compacted densities, have greater shear strength, lower permeability, and less settlement under load compared to uniformly graded soils. The D10 size (effective size) is used to estimate hydraulic conductivity through correlations like the Hazen formula. Grain size distribution is the primary basis for USCS soil classification and directly influences filter design criteria for earth dams, drainage systems, and erosion control.

How do I get the most accurate result?

Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.

What inputs do I need to use Grain Size Uniformity Coefficient Calculator accurately?

Each field is labelled with the required unit (metric or imperial). Gather your source values before starting โ€” for example, a weight measurement in kilograms, a distance in metres, or a dollar amount โ€” and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.

References

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