What is Young's modulus?

Young's modulus (E) is the ratio of tensile stress to tensile strain in a material within its elastic region. It measures stiffness — a higher value means less deformation under load. Steel has E ≈ 200 GPa; rubber is around 0.01–0.1 GPa.

What units should I use for inputs?

Force in Newtons (N), area in m² or mm² (the tool converts automatically), lengths in meters. The output unit for modulus and stress can be switched between Pa, MPa, and GPa.

What is the difference between stress and strain?

Stress (σ) is force per unit area (Pa). Strain (ε) is the fractional change in length — it is dimensionless. Young's modulus relates the two: E = σ/ε.

Why does the calculator require me to leave one field blank?

The tool solves for the missing quantity using the relationship E = (F/A) / (ΔL/L₀). If you fill all fields it will check consistency instead and report any discrepancy.

What is the elastic limit?

Young's modulus only applies below the material's elastic (proportional) limit. Beyond that, permanent deformation (plastic strain) occurs and Hooke's law no longer holds.

Young's Modulus Calculator

Enter force, area, elongation, and original length to calculate Young's modulus, stress, or strain. Solve for any one unknown.

Inputs

Leave the field you want to solve for blank. Fill in all others.

Young's Modulus (E)

Applied Force (F) — N

Cross-sectional Area (A)

Original Length (L₀) — m

Elongation (ΔL) — m

Results

Fill in the inputs above and click Calculate.

Formula Reference

E= σ / ε = (F / A) / (ΔL / L₀)

σ= F / A [Pa]

ε= ΔL / L₀ [dimensionless]

Material Reference Table

Click a row to pre-fill the modulus field. Values are typical ranges.

Material	E (GPa)	Notes

Summary

This calculator computes Young's modulus (E), tensile stress (σ), or strain (ε) given force, cross-sectional area, elongation, and original length. Leave one field blank and the tool solves for it. A reference table of common engineering materials is included for quick lookup.

How it works

Young's modulus E = stress / strain = (F/A) / (ΔL/L₀).
Stress σ = F / A, where F is force (N) and A is cross-sectional area (m²).
Strain ε = ΔL / L₀, where ΔL is elongation and L₀ is original length.
Leave exactly one field blank; the calculator solves for that unknown.
Switch output units between Pa, MPa, and GPa using the unit selector.

Use cases

Verify experimental tensile test data against a material's expected modulus.
Calculate how much a steel rod stretches under a known load.
Determine the cross-sectional area required to keep strain within design limits.
Back-calculate stress from measured elongation when modulus is known.
Compare stiffness of aluminum vs. titanium for a lightweight structural application.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu