Stress • Strain • Young’s Modulus • Poisson’s Ratio

CE Style

Inputs

Enter as a ratio (e.g., 0.001 = 0.1%)

Key Results

Details & Derived

Uniaxial: σ = E·ε. Poisson: ν = −εlat/εax. Plane stress: εx=(σx−νσy)/E, εy=(σy−νσx)/E, γxy=τxy/G, with G=E/[2(1+ν)].

How to use this calculator

Boost Guide

Quick start

  1. Select Units (SI or Imperial).
  2. Pick a Mode: Uniaxial (solve any of σ, ε, E, ν) or Plane stress (ε from σ, E, ν).
  3. Enter the requested inputs for the selected Solve for target.
  4. Click Calculate to see key results and derived moduli.
Core relations: σ = E·ε, ν = −εlat/εax, G = E / [2(1+ν)], K = E / [3(1−2ν)].

Modes

  • Uniaxial: Solve one of {σ, ε, E, ν}. Optionally provide ν to also get G and K.
  • Plane stress: Provide E, ν, and in-plane stresses σx, σy, τxy to compute εx, εy, γxy and G, K.

Inputs

  • Units: SI shows MPa/GPa; Imperial shows ksi/Mpsi.
  • Uniaxial (solve σ): Need E and ε.
  • Uniaxial (solve ε): Need E and σ.
  • Uniaxial (solve E): Need σ and ε (ε ≠ 0).
  • Uniaxial (solve ν): Need axial and lateral strains (ν = −εlat/εax).
  • Plane stress: Need E, ν, σx, σy, τxy.
  • Strain entry: Enter as a ratio (e.g., 0.001 = 0.1%).

Results

  • Uniaxial: Solved variable (σ/ε/E/ν), plus optional G, K, and lateral strain if ν is provided.
  • Plane stress: εx, εy, γxy, and derived G, K. Inputs are echoed for traceability.
  • Strains are shown as ratio and in µε for readability.

Examples

  • Steel (uniaxial σ): E = 210 GPa, ε = 0.001 → σ = 210 MPa.
  • Find ε: E = 70 GPa, σ = 140 MPa → ε = 0.002 (2000 µε).
  • Plane stress: E = 210 GPa, ν = 0.30, σx = 120 MPa, σy = 40 MPa, τxy = 30 MPa → compute εx, εy, γxy and G ≈ 80.8 GPa.

Notes & limits

  • Small-strain, linear-elastic assumptions; plasticity, creep, and large strains are not modeled.
  • Physically reasonable range: 0 ≤ ν < 0.5 for most isotropic solids.
  • Units are consistent per your selection; conversions are handled internally.
  • Plane stress assumes σz = 0 (thin plates); use with care for thick bodies.
FAQ & Troubleshooting

Why do I see “–” instead of numbers?

  • One or more required inputs are blank or non-numeric. Fill the fields shown for the selected solve mode.

Units look off

  • Switch Units first; then enter values (e.g., 200 MPa vs 29 ksi).

Strain entry

  • Enter as a ratio: 0.001 = 0.1% = 1000 µε.

Impossible ν?

  • Check signs: in tension, lateral strain is typically negative → ν = −εlat/εax.
  • Most materials: 0.2–0.4. Values ≥ 0.5 are non-physical for isotropic elastic solids.

γxy seems large/small

  • It depends on G = E/[2(1+ν)]; verify E and ν for your material.

Copy-Paste Mini Workflow

1) Choose Units (SI/Imperial)
2) Pick Mode: Uniaxial / Plane stress
3) Choose “Solve for” (if Uniaxial)
4) Fill the requested inputs
5) Press Calculate
6) Read results (σ, ε, E, ν) and derived G, K; plane stress gives εx, εy, γxy