About the S-Wave Velocity Calculator
This tool calculates one unknown in the shear-wave relationship using shear modulus, density, and S-wave velocity. It is useful for students, geophysicists, engineers, and materials analysts who need a quick elastic-wave estimate for a solid material.
How to use this calculator
- Choose whether to solve for S-wave velocity, shear modulus, or density.
- Enter the two visible known values in the displayed units.
- Use GPa for shear modulus, kg/m³ for density, and m/s for velocity.
- Click Calculate to compute the missing value and velocity conversions.
- Click Reset to restore the default example values.
How it works
The calculator is based on the elastic shear-wave equation Vs = √(G / ρ), where Vs is S-wave velocity in meters per second, G is shear modulus in pascals, and ρ is density in kilograms per cubic meter.
When solving for velocity, the entered shear modulus is converted from GPa to Pa, then divided by density, and the square root is taken. When solving for shear modulus, the calculator rearranges the equation to G = ρ × Vs² and reports the result in GPa. When solving for density, it uses ρ = G / Vs².
The km/s and ft/s outputs are unit conversions of the velocity value used in the calculation. This educational calculator assumes an isotropic, homogeneous elastic solid, so real field values may differ because of fractures, saturation, pressure, temperature, anisotropy, or layering.
Example calculation
Using the default values, solve for S-wave velocity with G = 30 GPa and ρ = 2700 kg/m³. Convert 30 GPa to 30,000,000,000 Pa, then compute Vs = √(30,000,000,000 / 2700) = 3333.33 m/s, which is 3.3333 km/s or about 10,936.13 ft/s.
Frequently asked questions
What units should I use for shear modulus?
Enter shear modulus in GPa. The calculator converts it internally to pascals before applying the formula.
Why must all inputs be greater than zero?
The shear-wave equation requires positive modulus, density, and velocity values. Zero or negative values are not physically valid for this calculation.
Can S-waves travel through liquids?
Ideal liquids have no shear modulus, so they do not support S-waves in the same way solids do. This calculator is intended for elastic solids.
How do I calculate shear modulus from S-wave velocity?
Select the option to solve for shear modulus, then enter density and S-wave velocity. The calculator uses G = ρ × Vs² and reports G in GPa.
Are these results exact for rocks underground?
They are idealized estimates. Actual subsurface S-wave velocity can vary with rock fabric, cracks, fluids, pressure, temperature, anisotropy, and layering.