Stress, Strain, Young's Modulus & Factor of Safety formulas (PL / AE)

Engineer's unit shortcut: 1 Newton / mm² equals 1 Megapascal (MPa) exact!

Structural and mechanical engineers love working in Newtons (N) and millimeters (mm) because 1 N / 1 mm² = 10⁶ N / m² = 1 MPa exact—eliminating 10⁻⁶ area-conversion mistakes! On a structural steel tie-rod with Cross-Sectional Area B2 = 200 mm², Original Length C2 = 2,000 mm, Young's Modulus D2 = 200 GPa (200,000 MPa), and Yield Strength E2 = 250 MPa carrying Axial Load A2 = 25,000 N (25 kN):

Working Tensile Stress σ = P / A = 25,000 / 200 = 125.0 MPa; Yield Factor of Safety FoS = σ_yield / σ = 250 / 125 = 2.00; and Hooke's-Law Elastic Elongation ΔL = (P × L) / (A × (E_GPa × 1000)) = (25,000 × 2,000) / (200 × 200,000) = 1.2500 mm!

PL/AE assumes a uniform member under axial tension with small, linear-elastic deformation, constant cross section and modulus. It does not account for bending, stress concentrations, fatigue, buckling, connections or temperature effects. A calculated yield ratio is not a design approval or a universal safety threshold.

Tensile Stress (MPa), Elastic Elongation ΔL (mm), and Factor of Safety formulas

Multiplying D2 (GPa) by 1,000 converts Young's Modulus into MPa (N/mm²) to match Force (N) and Area (mm²).

=IF(OR(COUNT(A2:E2)<>5,A2<0,B2<=0,C2<=0,D2<=0,E2<=0),"Invalid inputs",IF(A2/B2>=E2,"Outside elastic model",ROUND(A2*C2/(B2*D2*1000),4)))

Tensile Stress (MPa) and Yield Factor of Safety

A ratio below 1 means the calculated nominal tensile stress exceeds the supplied yield strength. Linear-elastic elongation is then outside its intended model; required design margins depend on the application.

=IF(OR(COUNT(A2:E2)<>5,A2<0,B2<=0,C2<=0,D2<=0,E2<=0),"Invalid inputs",IF(A2=0,"No applied load",ROUND(E2/(A2/B2),2)))

Further reading

• Microsoft Support — ROUND function
• OpenStax — Elasticity and plasticity