Shear Wave Velocity Calculator
Find the shear wave velocity of soil or rock from its shear modulus and density, from Young's modulus and Poisson's ratio, or as Vs30 for a layered site.
🌍 What is Shear Wave Velocity?
Shear wave velocity, written Vs, is the speed at which a shear wave (an S-wave) travels through a solid. In a shear wave the material moves sideways, at right angles to the direction the wave travels, so the wave only exists where the material can resist being sheared. The speed depends on just two properties of an isotropic solid: the shear modulus G, which measures the stiffness against shear, and the density ρ, which measures the inertia. The relation is Vs = √(G / ρ). A stiffer material carries the wave faster, and a heavier one slows it down.
The number is used widely. Geotechnical and earthquake engineers measure Vs in the ground because it tracks the small-strain stiffness of soil and rock, and building codes classify sites by the average velocity of the top 30 m, called Vs30. Geophysicists use Vs and the ratio Vp/Vs to identify rock type and fluid content. Civil engineers use it for machine foundation design and liquefaction screening, and materials engineers use shear wave speed in ultrasonic testing of metals and concrete. Because a liquid has no shear stiffness, S-waves cannot pass through water or the liquid outer core of the Earth, which is how seismology learned about the core.
A few points are worth keeping straight. First, this page is about the shear wave itself. The Speed of Sound in Solids Calculator returns longitudinal, shear and thin rod speeds for engineered materials, while this tool adds soil and rock presets, the shear modulus from Young's modulus and Poisson's ratio, and the Vs30 site classification. Second, the modulus must be the right one: seismic velocity reflects the small-strain modulus G max, which is larger than the secant modulus measured at the strains of a foundation load. Third, the formulas assume an isotropic, linear elastic medium, so layered or fractured rock may show different speeds in different directions.
The calculator has three modes. From shear modulus gives Vs, the speed in km/s and ft/s, the time to travel 30 m and the shear impedance. From Young's modulus converts E and Poisson's ratio to G, then gives Vs, the P-wave speed, Vp/Vs, the bulk modulus and the P-wave modulus. Vs30 profile combines up to four layers into the time averaged Vs30 and a NEHRP site class, with a table of travel times. Each mode has its own chart.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Dense Sand from Shear Modulus
ρ = 1900 kg/m³, G = 120 MPa
Example 2 — Granite
ρ = 2700 kg/m³, G = 30 GPa
Example 3 — Concrete from Young's Modulus
E = 30 GPa, ν = 0.2, ρ = 2400 kg/m³
Example 4 — Soft Saturated Clay
E = 43.5 MPa, ν = 0.45, ρ = 1500 kg/m³
Example 5 — Vs30 of a Three Layer Site
5 m at 150 m/s, 10 m at 250 m/s, 20 m at 500 m/s (only 15 m of the last layer count)
Example 6 — Shallow Profile Extended to 30 m
10 m at 200 m/s over 5 m at 800 m/s (profile ends at 15 m)
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for shear wave velocity?
Shear wave velocity is Vs = sqrt(G / rho), where G is the shear modulus in pascals and rho is the density in kg/m3. For G = 120 MPa and rho = 1900 kg/m3, Vs = sqrt(1.2e8 / 1900) = 251.3 m/s.
How do I get shear wave velocity from Young's modulus?
First find G = E / (2 (1 + nu)) using Poisson's ratio nu, then Vs = sqrt(G / rho). For E = 30 GPa, nu = 0.2 and rho = 2400 kg/m3, G = 12.5 GPa and Vs = 2282 m/s. The Young's modulus mode does both steps.
What is Vs30?
Vs30 is the time averaged shear wave velocity of the top 30 m, Vs30 = 30 / sum(h_i / Vs_i). It is used in seismic codes to classify a site. A profile with 5 m at 150 m/s, 10 m at 250 m/s and 15 m at 500 m/s gives 290.3 m/s.
What are the NEHRP site classes by Vs30?
Class A is above 1500 m/s, B is 760 to 1500 m/s, C is 360 to 760 m/s, D is 180 to 360 m/s and E is below 180 m/s. Class F needs a site specific study. The calculator applies these boundaries to the Vs30 you compute.
What if the profile is shallower than 30 m?
A common convention is to extend the deepest layer velocity down to 30 m. The calculator does this and says so in the note, because it tends to give a conservative, lower Vs30 when a stiffer layer lies below the data.
Why is the S-wave slower than the P-wave?
A P-wave depends on the P-wave modulus (the bulk and shear stiffness together) while an S-wave depends only on the shear modulus. For nu = 0.25 the ratio Vp / Vs is 1.732, and shear waves typically travel at roughly half to 60 percent of the P-wave speed.
Can a shear wave travel through water or liquid?
No. A liquid has zero shear modulus, so Vs = 0 and S-waves cannot propagate in it. This is why S-waves do not pass through the liquid outer core of the Earth, while P-waves do.
What is a typical shear wave velocity for soft clay?
Soft soils are usually below 180 m/s. The soft clay preset uses an illustrative G of 15 MPa and density of 1500 kg/m3, which gives 100 m/s. Real values vary widely with stress, plasticity and depth, so treat presets as a rough guide.
How is this different from the Speed of Sound in Solids Calculator?
The Speed of Sound in Solids Calculator reports longitudinal, shear and thin rod speeds for engineered materials such as steel and glass. This page focuses on the shear wave: it works from G or E and nu, offers soil and rock presets, and adds Vs30 site classification with a layered profile.
What units should the shear modulus be in?
Any of Pa, kPa, MPa or GPa. The selector only tells the calculator how to read the number you type, so choosing GPa and typing 30 means 30 GPa. Internally G is converted to pascals before taking the square root.
Why does Vp / Vs blow up near a Poisson's ratio of 0.5?
As nu approaches 0.5 the material becomes incompressible and the P-wave modulus grows without limit while G stays finite. Water saturated soils behave this way, so measured Vp there reflects the water, and Vs is the better indicator of the soil skeleton stiffness.