Young's Modulus & Stress-Strain Calculator

Young’s modulus (also called the elastic modulus) describes how stiff a material is — how much it resists being stretched or compressed. Named after Thomas Young who formalized it in 1807, it appears in virtually every structural engineering calculation.

The definitions

Stress (sigma, Pa) = Force (N) / Cross-section area (m^2)

Strain (epsilon, dimensionless) = Change in length (m) / Original length (m)

Young’s modulus E (Pa) = Stress / Strain

Equivalently: delta_L = F x L0 / (E x A)

This gives you the elongation of a rod of material under a given tensile or compressive force.

Typical values

Rubber: 0.01-0.1 GPa. Wood (along grain): 1-15 GPa. Bone: 14-20 GPa. Concrete: 25-30 GPa. Aluminum: 69 GPa. Steel: 190-210 GPa. Diamond: 1,000-1,200 GPa.

Elastic vs plastic deformation

This formula only holds in the elastic region — where the material returns to its original shape when the force is removed. Beyond the yield stress, materials deform permanently (plastic deformation). Steel yields at roughly 250-500 MPa; aluminum at 100-400 MPa. If your calculated stress exceeds the yield stress of the material, the formula no longer applies and the part is yielding.

The modulus is also temperature-dependent. Steel at 300°C has about 30% lower modulus than at room temperature, which is why fire causes structural steel to sag rather than snap.

Using this calculator

Enter the geometry and force to calculate stress, strain, and deformation. Or enter stress and strain directly to back-calculate the Young’s modulus of a material you are testing.