Elastic Equation Calculator

Built for beams, shafts, and test coupons. Switch between normal, shear, or bulk elasticity modes. See computed stresses, strains, and energy density instantly below.

Pick the relation that matches your loading.
Provide the other two inputs.
Used for lateral strain and derived moduli.
Young’s modulus for the material.
ε = ΔL/L, typically small in linear range.
Leave blank if solving for stress.

Example data table

Material Modulus E (GPa) Strain (με) Computed stress (MPa) Comment
Steel (typical) 200 500 100 Within many linear-elastic ranges.
Aluminum (typical) 70 800 56 Useful for light structures and frames.
Rubber (order-of-magnitude) 0.01 20000 0.2 Large strain; linear model may fail.
These are illustrative values for quick checks, not specifications.

Formula used

  • Normal elasticity (Hooke): σ = E · ε
  • Shear elasticity: τ = G · γ
  • Bulk elasticity: p = K · εᵥ
  • Elastic energy density: u = ½ · stress · strain (applies per mode)
The calculator rearranges each relation to solve for the selected unknown. For Poisson effects (normal mode), it uses ε_lat = −ν · ε_ax and a small-strain volumetric approximation.

How to use this calculator

  1. Select an elasticity mode that matches your problem.
  2. Choose what to solve for (stress/strain/modulus).
  3. Enter the other two values, and select their units.
  4. Optionally enter Poisson’s ratio for normal mode outputs.
  5. Click Calculate to show results above the form.
  6. Use Download CSV or Download PDF to export.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.