Young Modulus Calculator

What Is Young's Modulus?

Young's modulus (E) measures how stiff a material is in the elastic region, where it returns to its original shape after the load is removed. Our Young's Modulus Calculator can solve for E, for stress, or for strain, and it can also derive E from a measured force and change in length.

How the Calculation Works

$$\sigma = \frac{F}{A}, \qquad \varepsilon = \frac{\Delta L}{L_0} = \frac{L - L_0}{L_0}, \qquad E = \frac{\sigma}{\varepsilon}$$

Where:

• σ is the tensile stress in pascals
• F is the applied force in newtons
• A is the original cross-sectional area in square meters
• ε is the dimensionless longitudinal strain
• L₀ is the initial length and L is the final length
• E is Young's modulus, usually reported in gigapascals

Worked Example

A 100 N force is applied to a specimen with a cross-section of 0.0002 m², so σ = 100 / 0.0002 = 500,000 Pa. If the length changes from 0.5 m to 0.502 m, then ε = 0.002 / 0.5 = 0.004. Dividing gives E = 500,000 / 0.004 = 125,000,000 Pa, or about 0.125 GPa, a typical value for a soft polymer.

Related tools include the True Strain Calculator and the Work and Power Calculator.