# Elastic Constants Calculator

URL: https://speedycalculator.com/calculators/physics/elastic-constants/
Last updated: 2026-10-30

> The elastic constants calculator converts between the elastic constants of an isotropic material – Young's modulus E, shear modulus G, bulk modulus K, Poisson's ratio ν, Lamé's first parameter λ and the P-wave modulus M – from any known pair.

## Inputs

- Known pair
- Young's modulus E (GPa, MPa, Pa, psi, Mpsi)
- Poisson's ratio ν
- Shear modulus G (GPa, MPa, Pa, psi, Mpsi)
- Bulk modulus K (GPa, MPa, Pa, psi, Mpsi)

## Results

- Young's modulus E
- Poisson's ratio ν
- Shear modulus G
- Bulk modulus K
- Lamé's first parameter λ
- P-wave modulus M

## Formula

```
G = E/(2(1 + ν)),  K = E/(3(1 − 2ν)),  λ = Eν/((1 + ν)(1 − 2ν)),  M = E(1 − ν)/((1 + ν)(1 − 2ν))
```

## Explanation

An isotropic elastic material is fully described by just two constants. Once you know any pair, all the others follow. Engineers, seismologists and simulation users switch between them constantly.

### How to use the Elastic Constants Calculator

- **Known pair**
- **Young's modulus E**
- **Poisson's ratio ν**
- **Shear modulus G**
- **Bulk modulus K**

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

### How it works

Choose which pair you know and enter the values.

### Inputs explained

FieldWhat to enterKnown pairChoose one: E and ν, E and G, K and G, E and KYoung's modulus EUnits: GPa, MPa, Pa, psi, MpsiPoisson's ratio νA numberShear modulus GUnits: GPa, MPa, Pa, psi, MpsiBulk modulus KUnits: GPa, MPa, Pa, psi, Mpsi

### What each result means

- **Young's modulus E** = [E]
- **Poisson's ratio ν** = [nu]
- **Shear modulus G** = [E]÷(2×(1 + [nu]))
- **Bulk modulus K** = [E]÷(3×(1 - 2×[nu]))
- **Lamé's first parameter λ** = [E]×[nu]÷((1 + [nu])×(1 - 2×[nu]))
- **P-wave modulus M** = [E]×(1 - [nu])÷((1 + [nu])×(1 - 2×[nu]))

### Example values

How the main result changes when **Young's modulus E** changes and everything else stays at the example values above:

Young's modulus E (GPa)Shear modulus G (GPa)10038.461515057.692320076.923125096.1538300115.3846400153.8462

## Worked example

Inputs — Known pair: E and ν; Young's modulus E: 200 GPa; Poisson's ratio ν: 0.3.

Results — Young's modulus E = 200 GPa; Poisson's ratio ν = 0.3; **Shear modulus G = 76.92308 GPa**; Bulk modulus K = 166.66667 GPa; Lamé's first parameter λ = 115.38462 GPa; P-wave modulus M = 269.23077 GPa.

## Key terms

- **Lamé parameters**: λ and μ (= G), used in the theory of elasticity.

## FAQ

**Why are only two constants needed?**
Isotropic linear elasticity has two independent parameters.

**What range can Poisson's ratio take?**
Between −1 and 0.5 for stable isotropic materials.

**What happens as ν approaches 0.5?**
The material becomes incompressible and K tends to infinity.

**Where is the P-wave modulus used?**
In seismology – it sets the speed of compression waves.


## 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/)