Void Ratio Calculator
Free Void ratio Calculator for soil & sediment mechanics. Enter variables to compute results with formulas and detailed steps.
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Void ratio equals the volume of voids divided by the volume of solids. It can also be calculated from porosity: e = n / (1 - n), or from dry density: e = (Gs x gamma_w / gamma_d) - 1, where Gs is specific gravity of solids and gamma_w is the unit weight of water.
Last reviewed: December 2025
Worked Examples
Example 1: Sandy Soil Sample
Example 2: Soft Clay Analysis
Background & Theory
The Void Ratio 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) − 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 (0–12) 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 (1–10), 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 5–7 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 × exp(−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 Void Ratio 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 — 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
Void Ratio (e) = Vv / Vs
Void ratio equals the volume of voids divided by the volume of solids. It can also be calculated from porosity: e = n / (1 - n), or from dry density: e = (Gs x gamma_w / gamma_d) - 1, where Gs is specific gravity of solids and gamma_w is the unit weight of water.
Worked Examples
Example 1: Sandy Soil Sample
Problem: A soil sample has void volume of 35 cm3 and solid volume of 65 cm3.
Solution: Void Ratio = Vv / Vs = 35 / 65 = 0.538\nPorosity = Vv / (Vv + Vs) = 35 / 100 = 35%\nDry Density = (2.65 / (1 + 0.538)) x 1000 = 1723 kg/m3\nThis is a medium-density sand.
Result: Void ratio: 0.538 | Porosity: 35% | Medium density
Example 2: Soft Clay Analysis
Problem: A clay sample has void volume of 55 cm3 and solid volume of 45 cm3. Gs = 2.70.
Solution: Void Ratio = 55 / 45 = 1.222\nPorosity = 55 / 100 = 55%\nDry Density = (2.70 / (1 + 1.222)) x 1000 = 1215 kg/m3\nHigh void ratio indicates a loose, compressible clay.
Result: Void ratio: 1.222 | Porosity: 55% | Loose/compressible
Frequently Asked Questions
What is void ratio in soil mechanics?
Void ratio (e) is the ratio of the volume of voids (air and water spaces) to the volume of solid particles in a soil sample. Unlike porosity, which relates voids to total volume, void ratio relates voids to solids only. It can exceed 1.0, meaning there is more void space than solid material. Typical values range from 0.3 for dense gravel to 1.5 for soft clay, though organic soils and marine clays can have void ratios exceeding 3.0.
How are void ratio and porosity related?
Void ratio (e) and porosity (n) are both measures of void space but use different references. They convert between each other using: e = n / (1 - n) and n = e / (1 + e). For example, a porosity of 40% (0.4) gives a void ratio of 0.667. While porosity is bounded between 0 and 1 (or 0-100%), void ratio can theoretically range from 0 to infinity. Geotechnical engineers generally prefer void ratio because it keeps the solid volume constant in the denominator during compression.
Why do geotechnical engineers prefer void ratio over porosity?
Engineers prefer void ratio because the solid volume (denominator) remains constant when soil is compressed, while the void volume (numerator) changes. This makes mathematical relationships simpler. When soil consolidates under load, the void ratio decreases linearly on a semi-log plot against stress, producing the well-known e-log(p) curve used in settlement calculations. Porosity changes are harder to work with because both the numerator and denominator change simultaneously during compression.
What void ratio values indicate good foundation soil?
For foundations, lower void ratios generally indicate stronger, less compressible soil. Dense sands with void ratios of 0.3-0.5 are excellent foundation materials with high bearing capacity and minimal settlement. Medium-density soils (e = 0.5-0.8) are acceptable for most structures. Loose soils with void ratios above 0.8 may require ground improvement. Clays with void ratios above 1.0 are highly compressible and prone to significant long-term settlement under loading.
How is void ratio measured in the laboratory?
Void ratio is typically determined from phase relationships using measured quantities. The most common method involves measuring the dry density of an undisturbed soil sample and the specific gravity of solids: e = (Gs * gamma_w / gamma_d) - 1. Alternatively, it can be found directly from volume measurements using a wax-coated sample for total volume and an oven-dried weight for solid volume. In consolidation tests, void ratio changes are tracked continuously as load is applied.
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy