# Shear Wave Velocity Calculator

URL: https://speedycalculator.com/calculators/physics/shear-wave-velocity/
Last updated: 2026-10-30

> The shear wave velocity calculator finds the speed of shear (S) waves in a solid from its shear modulus and density, with common materials and soils.

## Inputs

- Material
- Shear modulus G (GPa, MPa, Pa, psi, Mpsi)
- Density ρ (kg/m³, g/cm³, g/mL, lb/ft³, lb/in³)

## Results

- Shear wave velocity v_s
- Seismic site class (top 30 m, for soils/rock)

## Formula

```
v_s = √(G / ρ)
```

## Explanation

Shear waves move material sideways as they travel and cannot pass through liquids – which is how seismologists discovered that Earth's outer core is liquid. Engineers measure them to assess soil stiffness for earthquake design.

### How to use the Shear Wave Velocity Calculator

- **Material**
- **Shear modulus G**
- **Density ρ**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose a material or enter its shear modulus and density.

### Inputs explained

FieldWhat to enterMaterialChoose one: Structural steel, Aluminium, Copper, Glass …Shear modulus GUnits: GPa, MPa, Pa, psi, MpsiDensity ρUnits: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³

### Example values

How the main result changes when **Shear modulus G** changes and everything else stays at the example values above:

Shear modulus G (GPa)Shear wave velocity v_s (m/s)39.653,178.350359.473,178.350379.33,178.350399.133,178.3503118.953,178.3503158.63,178.3503

## Worked example

Inputs — Material: Structural steel.

Results — **Shear wave velocity v_s = 3,178.35033 m/s**; Seismic site class (top 30 m, for soils/rock) = A – hard rock.

## Key terms

- **S-wave**: A transverse (shear) elastic wave.

## FAQ

**Why can't S-waves travel through liquids?**
Liquids have no shear stiffness (G = 0).

**How fast are S-waves in rock?**
Typically 2–4 km/s.

**What is V_s30?**
The average shear-wave velocity in the top 30 m, used to classify building sites.

**How do S and P waves compare?**
S-waves are slower, roughly 0.6 times the P-wave speed.


## Sources

- [MIT OpenCourseWare – Mechanics of Materials](https://ocw.mit.edu/courses/2-001-mechanics-materials-i-fall-2006/)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)
- [USGS – Earthquake hazards](https://www.usgs.gov/programs/earthquake-hazards)