Skip to main content

Seismic Wave Velocity Calculator

Calculate seismic wave velocity with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.

Skip to calculator
Earth Science & Geology

Seismic Wave Velocity Calculator

Calculate P-wave and S-wave velocities from elastic moduli and density. Convert between bulk/shear modulus and Young modulus inputs.

Last updated: December 2025Reviewed by NovaCalculator Mathematics Team

Calculator

Adjust values & calculate

Set to 0 for fluids (no S-wave)

Understand the Math

Formula

Vp = sqrt((K + 4G/3) / rho) | Vs = sqrt(G / rho)

P-wave velocity depends on bulk modulus K, shear modulus G, and density rho. S-wave velocity depends only on shear modulus and density. These fundamental relationships connect elastic properties of rocks to seismic wave propagation speeds.

Last reviewed: December 2025

Worked Examples

Example 1: Granite P and S-wave Velocity

Calculate Vp and Vs for granite with K = 50 GPa, G = 30 GPa, density = 2650 kg/m^3.
Solution:
Vp = sqrt((50e9 + 4*30e9/3) / 2650) Vp = sqrt((50e9 + 40e9) / 2650) Vp = sqrt(3.396e7) = 5828 m/s Vs = sqrt(30e9 / 2650) = sqrt(1.132e7) = 3365 m/s
Result: Vp = 5828 m/s, Vs = 3365 m/s, Vp/Vs = 1.732

Example 2: Limestone from Young Modulus

Find velocities for limestone: E = 60 GPa, Poisson ratio = 0.28, density = 2700 kg/m^3.
Solution:
K = 60e9 / (3*(1-0.56)) = 45.45 GPa G = 60e9 / (2*(1.28)) = 23.44 GPa Vp = sqrt((45.45e9 + 4*23.44e9/3) / 2700) = 5395 m/s Vs = sqrt(23.44e9 / 2700) = 2946 m/s
Result: Vp = 5395 m/s, Vs = 2946 m/s
Expert Insights

Background & Theory

The Seismic Wave Velocity 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 Seismic Wave Velocity 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.

Share this calculator

Explore More

Frequently Asked Questions

Seismic wave velocity depends on the elastic properties and density of the medium. P-wave velocity Vp depends on the bulk modulus K (resistance to compression), shear modulus G (resistance to shearing), and density: Vp = sqrt((K + 4G/3)/rho). S-wave velocity depends only on shear modulus and density: Vs = sqrt(G/rho). Higher elastic moduli increase velocity, while higher density decreases it. In practice, the modulus effect dominates, so denser rocks generally have higher velocities because they also tend to be stiffer.
Common P-wave velocities include: water 1500 m/s, unconsolidated sand 200-800 m/s, sandstone 2000-4500 m/s, limestone 3500-6500 m/s, granite 5000-6500 m/s, basalt 5500-6500 m/s, and the Earth mantle 7800-13700 m/s. S-wave velocities are typically 50-70% of P-wave velocities for solid rocks. Velocities generally increase with depth due to increased confining pressure, which closes cracks and increases stiffness. Fluid saturation increases Vp but has little effect on Vs.
Poisson ratio (nu) is directly calculable from the Vp/Vs ratio: nu = ((Vp/Vs)^2 - 2) / (2*(Vp/Vs)^2 - 2). For most rocks, Poisson ratio ranges from 0.1 to 0.45. A ratio of 0.25 corresponds to Vp/Vs = 1.732. Fluid-saturated rocks tend to have higher Poisson ratios (0.3-0.4) than dry rocks. Gas-bearing sands often show anomalously low Vp/Vs ratios and Poisson ratios, making this measurement valuable for hydrocarbon detection in seismic exploration.
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.
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.
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.

Share this calculator

Formula

Vp = sqrt((K + 4G/3) / rho) | Vs = sqrt(G / rho)

P-wave velocity depends on bulk modulus K, shear modulus G, and density rho. S-wave velocity depends only on shear modulus and density. These fundamental relationships connect elastic properties of rocks to seismic wave propagation speeds.

Worked Examples

Example 1: Granite P and S-wave Velocity

Problem: Calculate Vp and Vs for granite with K = 50 GPa, G = 30 GPa, density = 2650 kg/m^3.

Solution: Vp = sqrt((50e9 + 4*30e9/3) / 2650)\nVp = sqrt((50e9 + 40e9) / 2650)\nVp = sqrt(3.396e7) = 5828 m/s\nVs = sqrt(30e9 / 2650) = sqrt(1.132e7) = 3365 m/s

Result: Vp = 5828 m/s, Vs = 3365 m/s, Vp/Vs = 1.732

Example 2: Limestone from Young Modulus

Problem: Find velocities for limestone: E = 60 GPa, Poisson ratio = 0.28, density = 2700 kg/m^3.

Solution: K = 60e9 / (3*(1-0.56)) = 45.45 GPa\nG = 60e9 / (2*(1.28)) = 23.44 GPa\nVp = sqrt((45.45e9 + 4*23.44e9/3) / 2700) = 5395 m/s\nVs = sqrt(23.44e9 / 2700) = 2946 m/s

Result: Vp = 5395 m/s, Vs = 2946 m/s

Frequently Asked Questions

What determines seismic wave velocity?

Seismic wave velocity depends on the elastic properties and density of the medium. P-wave velocity Vp depends on the bulk modulus K (resistance to compression), shear modulus G (resistance to shearing), and density: Vp = sqrt((K + 4G/3)/rho). S-wave velocity depends only on shear modulus and density: Vs = sqrt(G/rho). Higher elastic moduli increase velocity, while higher density decreases it. In practice, the modulus effect dominates, so denser rocks generally have higher velocities because they also tend to be stiffer.

What are typical seismic velocities for common rocks?

Common P-wave velocities include: water 1500 m/s, unconsolidated sand 200-800 m/s, sandstone 2000-4500 m/s, limestone 3500-6500 m/s, granite 5000-6500 m/s, basalt 5500-6500 m/s, and the Earth mantle 7800-13700 m/s. S-wave velocities are typically 50-70% of P-wave velocities for solid rocks. Velocities generally increase with depth due to increased confining pressure, which closes cracks and increases stiffness. Fluid saturation increases Vp but has little effect on Vs.

How is Poisson ratio related to wave velocities?

Poisson ratio (nu) is directly calculable from the Vp/Vs ratio: nu = ((Vp/Vs)^2 - 2) / (2*(Vp/Vs)^2 - 2). For most rocks, Poisson ratio ranges from 0.1 to 0.45. A ratio of 0.25 corresponds to Vp/Vs = 1.732. Fluid-saturated rocks tend to have higher Poisson ratios (0.3-0.4) than dry rocks. Gas-bearing sands often show anomalously low Vp/Vs ratios and Poisson ratios, making this measurement valuable for hydrocarbon detection in seismic exploration.

What inputs do I need to use Seismic Wave Velocity 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.

How accurate are the results from Seismic Wave Velocity Calculator?

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.

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 ยท Editorial policy