Stress Calculator — Normal Stress, Strain & Elongation

Formula

How this is calculated

Normal stress is the internal force per unit area acting perpendicular to a cross-section. When a structural member carries an axial load F, that force is distributed over its cross-sectional area A, giving a stress σ = F / A. Working in SI engineering units — force in newtons (N) and area in square millimetres (mm²) — the result is in N/mm², which equals megapascals (MPa). Tensile loads produce positive stress; compressive loads produce negative stress (the calculator returns the magnitude).

For materials in the elastic range (below the yield point), Hooke's law links stress to strain: ε = σ / E, where E is Young's modulus in GPa. Because σ is in MPa and E is entered in GPa, the conversion E_MPa = E_GPa × 1000 is applied internally. Strain is dimensionless — it represents the fractional change in length per unit length. Steel has E ≈ 200 GPa, aluminium ≈ 70 GPa, and concrete ≈ 25–30 GPa.

Multiplying strain by the member's original length L (in mm) gives the total elastic elongation or shortening δ = ε × L. This formula assumes a uniform cross-section and a centrally applied axial load along the full length. It does not account for stress concentrations at holes, notches, or section changes — for those cases, see the stress-concentration-factor calculator. It also assumes linear-elastic behaviour; once stress exceeds the yield strength, the material deforms plastically and the linear formulas no longer apply.