Elastic Moduli Converter E G K
Our geology & geophysics calculator computes elastic moduli e, g, k, accurately. Enter measurements for results with formulas and error analysis.
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For isotropic linear elastic materials, only two independent elastic constants are needed. All others can be derived. E = Young's Modulus, G = Shear Modulus, K = Bulk Modulus, v = Poisson's Ratio. Lambda (first Lame parameter) = K - 2G/3.
Last reviewed: December 2025
Worked Examples
Example 1: Steel Properties Conversion
Example 2: Sandstone from Seismic Data
Background & Theory
The Elastic Moduli Converter (e, G, K, ฮ) 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) โ 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 (0โ12) 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 (1โ10), 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 5โ7 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(โMgh / 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 Elastic Moduli Converter (e, G, K, ฮ) 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.
Frequently Asked Questions
Formula
E = 2G(1+v) = 3K(1-2v) = 9KG/(3K+G)
For isotropic linear elastic materials, only two independent elastic constants are needed. All others can be derived. E = Young's Modulus, G = Shear Modulus, K = Bulk Modulus, v = Poisson's Ratio. Lambda (first Lame parameter) = K - 2G/3.
Worked Examples
Example 1: Steel Properties Conversion
Problem: Steel has Young's Modulus E = 200 GPa and Poisson's Ratio v = 0.30. Calculate all other elastic moduli.
Solution: G = E / (2(1 + v)) = 200 / (2 x 1.30) = 76.92 GPa\nK = E / (3(1 - 2v)) = 200 / (3 x 0.40) = 166.67 GPa\nLambda = K - 2G/3 = 166.67 - 51.28 = 115.38 GPa\nM = K + 4G/3 = 166.67 + 102.56 = 269.23 GPa\nVp/Vs = sqrt(M/G) = sqrt(3.50) = 1.871
Result: G = 76.92 GPa | K = 166.67 GPa | Lambda = 115.38 GPa
Example 2: Sandstone from Seismic Data
Problem: A sandstone sample has Shear Modulus G = 12 GPa and Bulk Modulus K = 20 GPa. Determine E and Poisson's Ratio.
Solution: E = 9KG / (3K + G) = 9 x 20 x 12 / (60 + 12) = 2160 / 72 = 30 GPa\nv = (3K - 2G) / (2(3K + G)) = (60 - 24) / (2 x 72) = 36 / 144 = 0.25\nLambda = K - 2G/3 = 20 - 8 = 12 GPa\nVp/Vs = sqrt((K + 4G/3) / G) = sqrt(36/12) = 1.732
Result: E = 30 GPa | v = 0.25 | Vp/Vs = 1.732
Frequently Asked Questions
What are elastic moduli and why are they important in geology and engineering?
Elastic moduli are fundamental material properties that describe how a material deforms under stress and returns to its original shape when the stress is removed. The four primary elastic moduli are Young's Modulus (E), which measures resistance to axial stretching or compression; Shear Modulus (G), which measures resistance to shape change; Bulk Modulus (K), which measures resistance to uniform compression; and Poisson's Ratio, which describes how a material contracts laterally when stretched. In geology and geophysics, these parameters are essential for understanding seismic wave propagation, rock mechanics, reservoir characterization, and earthquake analysis. In engineering, they determine structural behavior under load and are critical for design calculations.
How are the different elastic moduli related to each other mathematically?
For isotropic, linearly elastic materials, only two independent elastic constants are needed to fully describe the material's elastic behavior. All other moduli can be derived from any known pair. The key relationships include: E = 2G(1 + v), which connects Young's Modulus to Shear Modulus and Poisson's Ratio; E = 3K(1 - 2v), which links Young's Modulus to Bulk Modulus and Poisson's Ratio; and G = E / (2(1 + v)), which derives Shear Modulus from Young's Modulus and Poisson's Ratio. The Lame parameters (lambda and mu, where mu equals G) provide an alternative description commonly used in seismology. These relationships assume the material is homogeneous and isotropic, meaning its properties are the same in all directions.
What are typical elastic moduli values for common rocks and minerals?
Rock elastic properties vary widely depending on composition, porosity, saturation, and confining pressure. Granite typically has a Young's Modulus of 40 to 70 GPa, Shear Modulus of 20 to 30 GPa, Bulk Modulus of 25 to 55 GPa, and Poisson's Ratio of 0.20 to 0.30. Sandstone ranges from 10 to 40 GPa for Young's Modulus depending on porosity and cementation. Limestone has Young's Modulus of 20 to 70 GPa. Shale is highly anisotropic but typically shows 5 to 30 GPa. Basalt has values of 50 to 100 GPa for Young's Modulus. These values increase with confining pressure and decrease with increasing porosity, temperature, and fluid saturation. In geophysics, dynamic moduli measured from seismic waves are typically higher than static moduli measured in laboratory tests.
How are elastic moduli used in seismic wave velocity calculations?
Elastic moduli directly control the velocities of seismic waves through Earth materials. The P-wave (compressional wave) velocity is calculated as Vp = sqrt((K + 4G/3) / rho), where rho is density. The S-wave (shear wave) velocity is Vs = sqrt(G / rho). The ratio Vp/Vs is related to Poisson's Ratio by the equation v = (Vp/Vs)^2 - 2) / (2((Vp/Vs)^2 - 1)). These relationships are fundamental in seismology for determining rock properties from seismic surveys, earthquake analysis, and reservoir characterization. AVO (Amplitude Versus Offset) analysis in petroleum exploration uses changes in elastic moduli at geological boundaries to predict fluid content and lithology from surface seismic data.
Why might my result differ from another tool or reference?
Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy