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
| Field | What to enter |
|---|---|
| Known pair | Choose one: E and ν, E and G, K and G, E and K |
| Young’s modulus E | Units: GPa, MPa, Pa, psi, Mpsi |
| Poisson’s ratio ν | A number |
| Shear modulus G | Units: GPa, MPa, Pa, psi, Mpsi |
| Bulk modulus K | Units: 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) |
|---|---|
| 100 | 38.4615 |
| 150 | 57.6923 |
| 200 | 76.9231 |
| 250 | 96.1538 |
| 300 | 115.3846 |
| 400 | 153.8462 |
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))
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.
Frequently asked questions
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.