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Young's Modulus Calculator

Measure of stiffness.

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Young's Modulus

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Overview

Young's Modulus, also known as the elastic modulus, quantifies the stiffness of a solid material by defining the relationship between tensile or compressive stress and axial strain. It represents the slope of the linear-elastic region on a stress-strain curve, indicating how much a material will elastically deform under a specific load.

Symbols

Variables

E = Young's Modulus, = Stress, = Strain

Young's Modulus
Pa
Stress
Pa
Strain
Variable

Apply it well

When To Use

When to use: Apply this equation when a material is undergoing elastic deformation, meaning it will return to its original shape once the load is removed. It is only valid within the linear portion of the stress-strain curve, specifically before the material reaches its proportional limit.

Why it matters: This value allows engineers to predict how structural components like beams, bridge cables, or aircraft wings will deflect under operational loads. Selecting materials with the appropriate modulus is critical for ensuring mechanical stability and preventing structural failure or excessive vibration.

Avoid these traps

Common Mistakes

  • Using plastic region data.
  • Mixing stress units.

One free problem

Practice Problem

A steel rod is subjected to a tensile stress of 200,000,000 Pa, resulting in a longitudinal strain of 0.001. Calculate the Young's Modulus of the steel.

Stress200000000 Pa
Strain0.001

Solve for:

Hint: Divide the stress by the strain.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Mechanics of Materials by Beer, Johnston, DeWolf, and Mazurek
  2. Wikipedia: Young's modulus
  3. Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (2007). Transport Phenomena (2nd ed.). John Wiley & Sons.
  4. Incropera, F. P., DeWitt, D. P., Bergman, T. L., & Lavine, A. S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.).
  5. IUPAC Gold Book: 'modulus of elasticity' (https://goldbook.iupac.org/terms/view/M03964)
  6. Wikipedia: 'Young's modulus' (https://en.wikipedia.org/wiki/Young%27s_modulus)
  7. Callister, W. D., & Rethwisch, D. G. Materials Science and Engineering: An Introduction
  8. Beer, F. P., Johnston, E. R., DeWolf, J. T., & Mazurek, D. F. Mechanics of Materials