Shear Wave Velocity Calculator
Enter the shear modulus and density of any material to instantly calculate the shear wave velocity (S-wave velocity). Six solve modes let you reverse-calculate the shear modulus, density, wavelength, or frequency, or derive Vs from Young's modulus and Poisson's ratio. Material presets for steel, concrete, granite, soil and fifteen other common materials speed up routine work. A NEHRP site-class table classifies your result for seismic design.
What is shear wave velocity?
Shear wave velocity (Vs or S-wave velocity) is the speed at which a shear wave - a transverse elastic wave where particle motion is perpendicular to the direction of propagation - travels through a solid medium. Unlike pressure waves (P-waves), shear waves cannot propagate through fluids, so they are confined to solids and are widely used to characterise rock and soil stiffness. The governing formula is Vs = sqrt(G / rho), where G is the shear modulus (resistance to shear deformation, in Pascals) and rho is the bulk density (kg/m3). Harder, stiffer materials have higher G and therefore higher Vs; loose soils have low G and low Vs. Typical values range from under 100 m/s in very soft saturated clay to over 6000 m/s in hard igneous rock.
How to use this calculator
Select a solve mode from the "Solve for" dropdown. The default mode calculates Vs from G and rho - pick a material preset to prefill typical values, then adjust as needed. In "Shear modulus" mode, enter a known Vs and density to back-calculate G. In "Density" mode, provide Vs and G to find rho. Wavelength and frequency modes use Vs = lambda x f. The Young's modulus + Poisson's ratio mode first derives G = E / [2(1 + nu)], then computes Vs. All modes also report acoustic impedance (Zs = rho x Vs) and the NEHRP seismic site class. Enter a frequency in the optional field to see the wavelength alongside the velocity for any primary mode.
Vs30 and seismic site classification
Vs30 is defined as 30 m divided by the total shear-wave travel time through the top 30 m of soil or rock: Vs30 = 30 / sum(di / Vsi), where di and Vsi are the thickness and shear velocity of each layer. Building codes worldwide - including ASCE 7, IBC, Eurocode 8, and NZS 1170.5 - use Vs30 to assign seismic site classes (A through F in the US/NZ framework; Soil A through E in Eurocode). Soft soils (Class D and E) can amplify ground shaking by factors of 2 to 5 relative to rock, so site class drives the design response spectrum and the seismic design forces on a structure. This calculator classifies a single-layer Vs directly, or you can enter the weighted-harmonic-average Vs for a layered profile.
Acoustic impedance and wave reflections
Acoustic (seismic) impedance is Zs = rho x Vs and is expressed in Rayleigh (kg/m2/s) or MRayl (10^6 Rayleigh). The reflection coefficient at a planar boundary between two layers depends on the impedance contrast: R = (Z2 - Z1) / (Z2 + Z1). A large impedance contrast - for example, between a soft sediment layer (low Zs) and underlying rock (high Zs) - produces strong reflections exploited in seismic reflection surveys for oil and gas exploration and engineering site investigations. Designing seismic sensors and geophones also requires matching impedances to maximise energy transfer. The calculator outputs Zs in MRayl so you can compare layers directly.
NEHRP / IBC Vs30 seismic site classes
| Site class | Description | Vs30 range (m/s) | Amplification |
|---|---|---|---|
| A | Hard rock | >1500 | Very low |
| B | Rock | 760-1500 | Low |
| C | Very dense soil/rock | 360-760 | Moderate |
| D | Stiff soil | 180-360 | High |
| E | Soft clay soil | <180 | Very high |
| F | Special soils | n/a | Site-specific |
Site classes defined by ASCE 7 and the International Building Code (IBC) using shear wave velocity averaged over the top 30 m of soil (Vs30). Class F requires site-specific analysis.
Frequently asked questions
What is the formula for shear wave velocity?
The fundamental formula is Vs = sqrt(G / rho), where G is the shear modulus in Pascals and rho is the density in kg/m3. The result is in m/s. You can also express G through Young's modulus E and Poisson's ratio nu: G = E / [2(1 + nu)], which gives Vs = sqrt(E / [2(1 + nu) x rho]). All three quantities are properties of the solid medium, so Vs is determined entirely by the material.
What is a typical shear wave velocity for soil?
Soft clay and loose saturated sand: 100-200 m/s. Stiff clay and dense sand: 200-400 m/s. Soft rock and weathered material: 400-800 m/s. Fresh hard rock (granite, basalt): 2000-4000 m/s. Steel has a shear wave velocity of about 3200 m/s. These ranges are why NEHRP/IBC site classes are defined between 180 m/s and 1500 m/s.
How is Vs30 calculated from multiple soil layers?
Vs30 uses the harmonic average (travel-time average) over exactly 30 m depth: Vs30 = 30 / sum(di / Vsi) for layers with thickness di and velocity Vsi. A fast top layer and a slow bottom layer together yield a Vs30 closer to the slow layer because travel time is dominated by slow material. This is why Vs30 is NOT a simple arithmetic average of layer velocities.
Why can shear waves not travel through water?
Shear waves require that the medium resist shear deformation. Fluids have no shear strength - they simply flow rather than deform elastically in shear - so the shear modulus G of a fluid is zero, and Vs = sqrt(0 / rho) = 0. In practice, S-waves are completely absorbed at the boundary of a fluid body. This property is used in geophysics: the absence of S-waves below a depth indicates a fluid-saturated zone, and this contrast is what distinguishes P-wave and S-wave seismic surveys.
What is acoustic impedance and why does it matter?
Acoustic impedance Zs = rho x Vs (in Rayleigh, or MRayl). When a seismic wave hits a boundary between two materials with different impedances, some energy is reflected and the rest transmitted. The larger the impedance contrast, the stronger the reflection. In seismic exploration this is what creates the reflections recorded at the surface. In non-destructive testing, impedance matching between the transducer and the test material determines how much energy is coupled into the specimen.
How does shear wave velocity relate to Poisson's ratio?
Poisson's ratio nu relates G to Young's modulus E through G = E / [2(1 + nu)]. For isotropic elastic solids, the ratio of P-wave velocity (Vp) to S-wave velocity (Vs) is Vp/Vs = sqrt[(2 - 2nu) / (1 - 2nu)]. Saturated soils have nu close to 0.5, making Vp/Vs very large (Vp >> Vs) because the pore water carries compression but not shear. Dry rock has nu around 0.25, giving Vp/Vs approximately 1.73. Measuring both velocities in a seismic survey therefore constrains Poisson's ratio and, with it, the saturation state of the subsurface.