Stress/Strain Calculator

Forward: find stress and strain from load. Reverse: find required load from a stress target.

Material Preset

Stress Unit

Force F (N)

Area A (m²)

Original Length L₀ (m)

ΔL measured (m)

Normal Stress σ = F/A2.0000 MPa

Strain ε = ΔL/L₀1.0000e-3

Elongation ΔL (from E·ε·L₀)0.0050 mm

Factor of Safety (yield/σ)125.000

Young's Modulus E200.0 GPa

Yield Strength σ_y250.00 MPa

Stress-Strain Diagram

What This Calculator Does

Stress and strain are the fundamental measures of material response under load. Normal stress σ = F/A quantifies load intensity. Strain ε = ΔL/L₀ measures deformation. Young's modulus E = σ/ε links them in the elastic range. This calculator provides both a forward mode (find stress from load) and a reverse mode (find the load or force needed to reach a target stress), plus material presets for the most common engineering materials.

It combines Force, Cross-sectional Area, Original Length, Change in Length ΔL to estimate Normal Stress σ, Strain ε, Young's Modulus E.

Formula & Method

Normal stress:

\sigma = \frac{F}{A}

Axial strain:

\varepsilon = \frac{\Delta L}{L_0}

Young's modulus:

E = \frac{\sigma}{\varepsilon} \implies \Delta L = \frac{\sigma L_0}{E} = \frac{F L_0}{A E}

Factor of safety:

FoS = \frac{\sigma_y}{\sigma}

Thermal stress:

\sigma_{thermal} = E \alpha \Delta T

Notation used in the formulas: $R$ = Normal Stress σ; $x_{1}$ = Force; $x_{2}$ = Cross-sectional Area; $x_{3}$ = Original Length; $x_{4}$ = Change in Length ΔL.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

Steel A36 rod under 50 kN load

F = 50,000 N, A = 500 mm² = 0.0005 m², L₀ = 2 m σ = 50,000/0.0005 = 100,000,000 Pa = 100 MPa E = 200 GPa → ε = 100×10⁶ / 200×10⁹ = 0.0005 ΔL = 0.0005 × 2 = 0.001 m = 1 mm FoS = 250 MPa / 100 MPa = 2.5 ✓

Aluminium 6061-T6 — find load for 50% of yield

Target σ = 0.5 × 276 MPa = 138 MPa, A = 800 mm² = 8×10⁻⁴ m² Required F = 138×10⁶ × 8×10⁻⁴ = 110,400 N = 110.4 kN ΔL (over 1 m) = (138×10⁶ × 1) / (68.9×10⁹) = 2.00 mm

Reference Book

Mechanics of Materials

SI Edition

Russell C. Hibbeler · Pearson

A standard reference for stress, strain, section properties, beam behavior, and material deformation.

View Book

Inputs Used

Force: Used directly in the calculation.
Cross-sectional Area: Used directly in the calculation.
Original Length: Used directly in the calculation.
Change in Length ΔL: Used directly in the calculation.

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