Elongation Calculator

The formula

σ = F ÷ A; ε = ΔL ÷ L; E = σ ÷ ε; ΔL = FL ÷ AE

Stiffness and strength are different properties

Young's modulus describes stiffness — how much a material deflects under load. Yield strength describes strength — the stress at which it stops springing back. They are independent, and confusing them is the most common error in material selection.

Steel and carbon fibre have similar stiffness while carbon fibre is several times stronger. Nylon is nearly as strong as mild steel in yield, yet seventy times less stiff, which is why a nylon component of the same size flexes visibly under a load steel would barely notice. Choose modulus for deflection limits and strength for failure limits.

Shear uses G, not E. For most metals G is about 38% of E, so a shear calculation done with Young's modulus underestimates the deflection by roughly a factor of two and a half.

Engineering strain divides by the original length; true strain integrates over the changing length and equals ln(1+ε). Below a few percent they agree closely, which is why elastic design ignores the distinction — but in metal forming, where strains reach tens of percent, the difference is large and true strain is the meaningful one.