What is engineering stress?

Engineering stress σ is the applied force F divided by the original (undeformed) cross-sectional area A: σ = F / A. It is expressed in Pascals (Pa) for SI or pounds per square inch (psi) for Imperial. Engineering stress assumes the cross-section does not change during loading, which is valid in the elastic range.

What is engineering strain?

Engineering strain ε is the change in length ΔL divided by the original gauge length L₀: ε = ΔL / L₀. It is dimensionless (m/m or in/in). Strain represents the fractional deformation of the specimen.

How is Young's modulus calculated?

Young's modulus (elastic modulus) E = σ / ε, valid in the linear-elastic (Hookean) region. It quantifies the stiffness of the material — a higher E means the material deforms less for the same applied stress. Typical values: steel ~200 GPa, aluminum ~70 GPa, concrete ~30 GPa.

What is the difference between engineering and true stress?

Engineering stress uses the original area A₀ throughout loading, while true stress uses the instantaneous cross-sectional area at each load increment. For small elastic strains (below ~1%), the two values are nearly identical. This calculator uses engineering (nominal) stress, which is standard for most design applications.

Stress-Strain Calculator

Enter force, area, and deformation to instantly compute engineering stress, engineering strain, and Young's modulus in SI or Imperial units.

Inputs

Unit System

Applied Force (N)

Cross-sectional Area (m²)

Original Gauge Length L₀ (m)

Change in Length ΔL (m)

Enter values and click Calculate

Formulas Used

Engineering Stress

σ = F / A — Force (N or lbf) divided by original cross-sectional area (m² or in²).

Engineering Strain

ε = ΔL / L₀ — Change in length divided by original gauge length (dimensionless).

Young's Modulus

E = σ / ε — Stress divided by strain (valid in the elastic/Hookean region).

Summary

This stress-strain calculator applies the fundamental equations of mechanics of materials to compute engineering stress (σ = F/A), engineering strain (ε = ΔL/L₀), and Young's modulus (E = σ/ε) for a material specimen under uniaxial (axial) load. It supports both SI units (Newtons, meters, Pascals) and Imperial units (pound-force, inches, psi). All computation runs in the browser — no data is sent to any server.

How it works

Select a unit system: SI (N, m, Pa) or Imperial (lbf, in, psi).
Enter the applied axial force F.
Enter the original cross-sectional area A of the specimen.
Enter the original gauge length L₀.
Enter the change in length ΔL (deformation) of the specimen.
Click Calculate to see engineering stress σ, engineering strain ε, and Young's modulus E.

Use cases

Determining the elastic modulus of a material from a tensile test.
Verifying hand calculations in mechanics of materials coursework.
Sizing axially loaded bars and rods in structural design.
Converting between stress, strain, and modulus during material selection.
Checking specimen deformation against allowable stress limits.
Teaching Hooke's Law and linear elasticity concepts in engineering courses.

Frequently Asked Questions

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