Elastic Modulus Calculator Formula

Understand the math behind the elastic modulus calculator. Each variable explained with a worked example.

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Formulas Used

Elastic Modulus (E)

modulus_gpa = stress / strain / 1000

Elastic Modulus

modulus_mpa = stress / strain

Variables

VariableDescriptionDefault
stressStress (sigma)(MPa)200
strainStrain (epsilon)0.001

How It Works

Young's Modulus (Elastic Modulus)

Young's modulus E is the slope of the linear portion of the stress-strain curve. It measures a material's stiffness, or resistance to elastic deformation.

Formula

E = sigma / epsilon

where sigma is the axial stress and epsilon is the axial strain (both in the elastic region). E is an intrinsic material property independent of geometry.

Worked Example

A steel specimen shows 200 MPa stress at 0.001 strain (0.1%) in the elastic region.

stress = 200strain = 0.001
  1. 01E = 200 MPa / 0.001
  2. 02E = 200,000 MPa = 200 GPa
  3. 03This is consistent with structural steel (E ≈ 200 GPa)

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