Shear Wave Velocity Calculator

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Use this calculator to find shear wave velocity, dynamic shear modulus, or travel time from material stiffness, density, distance, and unit choices.

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How to use our Shear Wave Velocity Calculator

  1. Choose a mode in What do you want to calculate?: Shear wave velocity, Dynamic shear modulus, or Travel time.
  2. Enter the visible required values only. In velocity mode, use Shear modulus (selected unit) and Density (selected unit). In modulus mode, use Shear wave velocity (selected unit) and Density (selected unit). In travel time mode, use Distance (selected unit) and Shear wave velocity (selected unit).
  3. Open Advanced options if needed and set Shear modulus unit, Density unit, Distance unit, Velocity unit, and Time output unit so they match your numbers.
  4. If you are reporting results for class or a lab, choose a Display format and set Significant figures to match your required precision.
  5. Click Calculate to see the main result plus SI check values such as Shear wave velocity (SI) or Dynamic shear modulus (SI).
  6. Sanity-check the result: higher Shear modulus (selected unit) should raise Shear wave velocity, higher Density (selected unit) should lower it, and larger Distance (selected unit) should increase Travel time.
  7. Read the Model note before using the result in a real project. It reminds you that the basic relation is for a solid, approximately elastic medium.

Definitions

Shear wave velocity: The speed of sideways vibration through a solid material, usually written as Vs.

Shear modulus: A measure of how strongly a solid resists shape change when it is sheared. It is also called rigidity.

Density: Mass per volume. In this calculator it must be greater than zero.

Dynamic shear modulus: The shear modulus implied by wave motion, found from density and shear wave velocity using the elastic-wave relation.

Travel time: The time a shear wave needs to move across the entered distance.

SI units: Standard metric units used for checking results here: Pa for modulus, kg/m^3 for density, m for distance, s for time, and m/s for velocity.

Display format: The way numbers are shown, such as decimal, scientific, or engineering notation.

Common mistakes and quick fixes

Mistake: Entering a value in Shear modulus (selected unit) as if it were GPa while Shear modulus unit is still set to Pa.
Fix: Change Shear modulus unit to match your number before calculating Shear wave velocity or Dynamic shear modulus .

Mistake: Typing density in g/cm^3 into Density (selected unit) while Density unit is set to kg/m^3.
Fix: Either convert the number yourself or switch Density unit to g/cm^3 so the calculator converts it correctly.

Mistake: Using Distance (selected unit) in travel time mode with feet entered while Distance unit is set to m.
Fix: Set Distance unit to ft or re-enter the distance in meters before finding Travel time .

Mistake: Entering 0 or a negative number for Density (selected unit) , Shear modulus (selected unit) , or Shear wave velocity (selected unit) .
Fix: Use positive physical values only. Zero or negative inputs are invalid for these fields and will block the calculation.

Mistake: Reading Shear wave velocity in ft/s or km/s and comparing it directly to Shear wave velocity (SI) without noticing the units are different.
Fix: Compare values only after checking the unit shown next to each output, or use Shear wave velocity (SI) for a direct m/s check.

Mistake: Using this tool for layered-profile averages such as Vs30 just because the output says Shear wave velocity .
Fix: Use this calculator only for the single-material formulas shown here. It does not compute profile averages or site class values.

Limitations & Key Assumptions / Boundary Conditions

  • The main relation assumes a solid material that can sustain shear. It is not appropriate for fluids in the same way because fluids do not support shear deformation like solids do.
  • The formulas use a simple elastic-material model. Real materials may be anisotropic, layered, fractured, nonlinear, saturated, temperature-dependent, or frequency-dependent, so measured field values can differ.
  • Shear wave velocity and Dynamic shear modulus are only physically meaningful here when the required inputs are positive after unit conversion.
  • Travel time is computed as distance divided by velocity along a single path. It does not include refraction, reflections, changing velocity with depth, or curved travel paths.
  • This calculator handles one material state at a time. It does not compute Vs30, layered averages, site class, or full seismic site-response parameters.
  • Formatting choices such as Display format and Significant figures change how values are shown, not the underlying calculation.

Methodology

Core equations

The calculator uses three standard relations depending on the selected mode.

Vs = sqrt(G / ρ)

G = ρ x Vs^2

t = d / Vs

Here, Vs is shear wave velocity, G is shear modulus, ρ is density, t is travel time, and d is distance. The first relation is the usual elastic-solid formula for shear-wave speed [4].

Unit handling

All inputs are converted to SI units first, then the result is converted to the chosen display unit.

1 GPa = 1 x 10^9 Pa

1 psi = 6894.757293 Pa

1 g/cm^3 = 1000 kg/m^3

1 lb/ft^3 = 16.018463 kg/m^3

1 ft = 0.3048 m

1 m/s = 3.280839895 ft/s

1 s = 1000 ms

This keeps the math consistent even when the entry units are mixed.

Worked mini-example

If Shear modulus (selected unit) is 3.0 GPa and Density (selected unit) is 2500 kg/m^3, first convert 3.0 GPa to 3.0 x 10^9 Pa.

Vs = sqrt(3.0 x 10^9 / 2500) = 1095.445... m/s

So the calculator reports about 1095 m/s, or the same value in the selected velocity unit. If Distance (selected unit) is 10 m and velocity is 1200 m/s, then:

t = 10 / 1200 = 0.008333... s = 8.333... ms

Interpretation

A higher Shear wave velocity usually means the material is stiffer, less dense, or both. A higher Dynamic shear modulus means the entered density and velocity imply stronger resistance to shear deformation. A larger Travel time means the path is longer, the wave is slower, or both.

Validation and boundary conditions

The calculator rejects zero or negative density, zero or negative shear modulus, zero or negative velocity where required, and negative distance. Hidden fields are ignored in modes where they are not needed. If conversion or parsing produces an invalid number, the calculator shows an input error instead of a result.

Results are most reliable when the material behaves approximately like an isotropic elastic solid. For layered soils, strong anisotropy, or detailed seismic site work, this simple single-material model is only an approximation and should not be treated as a full profile analysis [2][3].

Sources

  1. Shear wave | Elasticity, Wave Motion & Vibration | Britannica – Encyclopedia Britannica
  2. Use of Shear Wave Velocity for Foundation Design | Geotechnical and Geological Engineering | Springer Nature Link – Springer
  3. Shear Wave Velocity Measurements [Final Report, Appendices] – BTS
  4. Shearwave Velocity for Settlement Calculations – Peter K. Robertson – Cpt-robertson