Young's Modulus Calculator

Understanding Young's Modulus Calculator

Young's modulus measures material stiffness, the ratio of stress to strain in the elastic region. Steel ≈ 200 GPa, aluminum ≈ 70 GPa.

How to use this calculator

1. Enter the stress value, usually in pascals, into the stress field.
2. Enter the strain value, which is unitless, into the strain field.
3. Check that both values are for the same loading condition, since stress and strain must match.
4. Read the calculated Young's modulus, and use it to compare material stiffness.

The formula explained

The calculator uses the formula \(E = \frac{\sigma}{\varepsilon}\), where \(E\) is Young's modulus. It computes stiffness by dividing stress by strain.

• E = Young's modulus, a measure of stiffness
• \(\sigma\) = stress, force per unit area
• \(\varepsilon\) = strain, the fractional change in length

Step by step method

1. Write down the stress \(\sigma\) and strain \(\varepsilon\).
2. Divide \(\sigma\) by \(\varepsilon\) using \(E = \frac{\sigma}{\varepsilon}\).
3. Keep the units of stress, so \(E\) is in pascals if stress is in pascals.
4. Interpret a larger \(E\) as a stiffer material.

Worked example

Problem. A metal sample has stress \(\sigma = 200000000\,\text{Pa}\) and strain \(\varepsilon = 0.001\). Find Young's modulus.

1. Use \(E = \frac{\sigma}{\varepsilon}\).
2. Substitute the values, \(E = \frac{200000000}{0.001}\).
3. Compute \(E = 200000000000\,\text{Pa}\).

Tips and common mistakes

• Strain must be unitless, so do not enter it as a percent unless the calculator specifically asks for percent.
• Use a positive strain value for tensile stretching, and make sure stress and strain come from the same test case.

Frequently asked questions