Shear Wave Velocity Calculator

A shear wave (also called an S-wave or secondary wave) is a type of mechanical wave in which particles oscillate perpendicular to the direction of wave propagation. Shear waves occur in solid bulk mediums under shear-type loading and are widely studied in seismology, geotechnical engineering, and non-destructive testing. Unlike compressional (P) waves, shear waves cannot propagate through liquids or gases.

Shear wave velocity (v_s) is the speed at which a shear wave travels through a material. It depends on the material's shear modulus (G) and density (ρ), and is given by v_s = √(G / ρ). Stiffer, less dense materials transmit shear waves faster. In geotechnical engineering, higher shear wave velocities generally indicate firmer, more stable ground.

Use the formula v_s = √(G / ρ), where G is the shear modulus in Pascals and ρ is the density in kg/m³. For example, copper has G ≈ 45 GPa and ρ ≈ 8,940 kg/m³, giving v_s = √(45,000,000,000 / 8,940) ≈ 2,243.6 m/s. Enter G in GPa and density in kg/m³ into this calculator and it handles the unit conversion automatically.

Titanium has a shear modulus of approximately 41 GPa and a density of about 4,507 kg/m³. Plugging these into v_s = √(G / ρ) gives roughly v_s ≈ 3,017 m/s. You can verify this by entering G = 41 GPa and ρ = 4507 kg/m³ in the calculator above.

Yes. Rearranging the formula gives G = v_s² × ρ. Select 'Calculate Shear Modulus from Velocity' in the Calculation Mode dropdown, then enter the known velocity and density. The calculator will return G in GPa.

Poisson's ratio (ν) is related to the shear modulus and Young's modulus by G = E / (2(1 + ν)). If you know Young's modulus and Poisson's ratio, you can derive G and then compute v_s. This calculator accepts E and ν as optional inputs and uses them to compute G when the primary G field is left blank.

Shear waves require a medium that can sustain shear stress, which only solid materials can do. Fluids (liquids and gases) have no shear stiffness — their shear modulus is effectively zero — so shear waves cannot propagate through them. This property is used in seismology to identify the liquid outer core of the Earth and in non-destructive testing to distinguish between solid and fluid phases.

Vs30 is the time-averaged shear wave velocity over the top 30 metres of ground, widely used in seismic hazard assessment and building code classification. It is calculated from individual layer velocities and thicknesses using Vs30 = 30 / Σ(dᵢ / Vsᵢ). Higher Vs30 values indicate stiffer, rockier ground that amplifies seismic shaking less than softer soils.