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Stress, Strain & Young's Modulus Calculator (Hooke's Law)

Calculate normal stress (MPa), axial strain (µε), Young's modulus of elasticity (E), and yield safety factor.

Input Parameters

kN
mm²

e.g. 200 mm² (16mm circular rod ≈ 201 mm²)

mm
mm
MPa

Structural Steel Grade 300/350 ≈ 300-350 MPa, Al 6061-T6 ≈ 275 MPa

Calculation Results

Normal Engineering Stress (σ)
250 MPa (36,260 psi)MPa
Axial Strain (ε)
0.0012 (1,200 µε / 0.12%)
Young's Modulus of Elasticity (E)
208.3 GPa (30.22 Mpsi)GPa
Yield Factor of Safety (FOS)
1.4× (Marginal Safety (FOS < 1.5))
Applied Force & Area
50 kN (50,000 N) over 200 mm²
Summary: An applied tensile force of 50 kN over 200 mm² creates an engineering stress of 250 MPa. An elongation of 0.6 mm over 500 mm yields an axial strain of 1200 µε, corresponding to a Young's Modulus of 208.3 GPa (Yield Factor of Safety: 1.4×).
Step-by-Step Calculation Solution
1.Normal Stress σ = Force ÷ Area = (50 × 1000 N) ÷ 200 mm² = 250 MPa
2.Axial Strain ε = ΔL ÷ L₀ = 0.6 mm ÷ 500 mm = 0.0012 (1200 µε)
3.Young's Modulus E = σ ÷ ε = 250 MPa ÷ 0.0012 = 208.33 GPa
4.Yield Factor of Safety = Yield Strength (350 MPa) ÷ Stress (250 MPa) = 1.4×

Formula & How Stress, Strain & Young's Modulus Calculator (Hooke's Law) Works

Mathematical Formula
Stress σ = F ÷ A | Strain ε = ΔL ÷ L₀ | Young's Modulus E = σ ÷ ε | Factor of Safety = σ_yield ÷ σ

Hooke's Law governs linear elastic deformation: within the elastic limit, normal stress is directly proportional to axial strain ($E = \sigma / \varepsilon$). Exceeding the yield strength results in permanent plastic deformation and structural failure.

How to Calculate Stress, Strain & Young's Modulus Calculator (Hooke's Law) (Step-by-Step)
  1. Enter Applied Force / Load (kN) (kN): Input your target parameter value.
  2. Enter Cross-Sectional Area (mm²) (mm²): Input your target parameter value.
  3. Enter Original Gauge Length L₀ (mm) (mm): Input your target parameter value.
  4. Enter Elongation / Deflection ΔL (mm) (mm): Input your target parameter value.
  5. Enter Material Yield Strength (MPa) (MPa): Input your target parameter value.
  6. Apply Formula: Calculate using Stress σ = F ÷ A | Strain ε = ΔL ÷ L₀ | Young's Modulus E = σ ÷ ε | Factor of Safety = σ_yield ÷ σ.
  7. Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)

What is the difference between stress and strain?

Stress ($\sigma$) is the internal force per unit area within a material (measured in MPa or psi), whereas Strain ($\varepsilon$) is the proportional deformation or elongation relative to original length (dimensionless).

Official Regulatory & Government Data Sources

Authoritative Standards & Verified Reference Citations

Independent & Verified

Calculations and mathematical logic on this page are grounded in published statutory rules, regulatory standards, and official government data published by the following bodies:

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