Stress Strain Calculator
Plan your materials project with our free stress strain calculator. Get precise measurements, material lists, and budgets.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
σ = F/A | ε = ΔL/L₀ | E = σ/ε | FoS = σ_yield / σ_working
Stress equals force divided by cross-sectional area. Strain equals the change in length divided by original length. Young's modulus (elastic modulus) is the ratio of stress to strain in the linear elastic region. Factor of safety is yield strength divided by working stress.
Worked Examples
Example 1: Steel Rod Under Tension
Problem:A steel rod (10mm diameter, 500mm long) stretches 0.25mm under a 15,700N tensile load. Calculate stress, strain, Young's modulus, and FoS (yield = 250 MPa).
Solution:Area = π(5mm)² = 78.54 mm²\nStress σ = 15700 / 78.54e-6 = 200 MPa\nStrain ε = 0.25/500 = 0.0005 (0.05%)\nYoung's Modulus E = 200/0.0005 = 400,000 MPa = 200 GPa ✓ (Steel)\nFoS = 250/200 = 1.25
Result:σ = 200 MPa | ε = 0.05% | E = 200 GPa | FoS = 1.25
Example 2: Aluminum Column Under Compression
Problem:An aluminum column (25mm × 25mm cross-section, 300mm long) shortens by 0.13mm under 44,850N compressive load. Yield strength = 276 MPa.
Solution:Area = 25 × 25 = 625 mm²\nStress σ = 44850 / 625e-6 = 71.76 MPa\nStrain ε = 0.13/300 = 0.000433 (0.043%)\nYoung's Modulus E = 71.76/0.000433 = 165,700 MPa ≈ 69 GPa ✓ (Aluminum)\nFoS = 276/71.76 = 3.85
Result:σ = 71.8 MPa | ε = 0.043% | E = 69 GPa | FoS = 3.85
Frequently Asked Questions
What is stress in engineering?
Engineering stress (sigma, σ) is the internal force per unit area within a material, caused by externally applied forces. It is calculated as σ = F/A, where F is the applied force (Newtons) and A is the cross-sectional area (m²). Stress is measured in Pascals (Pa) or commonly in Megapascals (MPa) for engineering materials. There are three main types: tensile stress (pulling apart), compressive stress (pushing together), and shear stress (sliding). Understanding stress is fundamental to structural design — every component must be designed so that the working stress remains safely below the material's yield strength.
What is strain?
Strain (epsilon, ε) is the measure of deformation representing the displacement between particles in a material. Engineering strain is calculated as ε = ΔL/L₀, where ΔL is the change in length and L₀ is the original length. Strain is dimensionless (no units) and is often expressed as a percentage or in microstrain (με = strain × 10⁶). Positive strain indicates elongation (tensile), negative strain indicates compression. Typical elastic strains in metals are very small, on the order of 0.001 to 0.01 (0.1% to 1%). Beyond the elastic limit, permanent plastic deformation occurs.
What is the difference between stress and pressure?
While both stress and pressure are force per unit area (Pa), they differ fundamentally. Pressure is an external force applied to a surface, is always compressive (pushes inward), is a scalar quantity (equal in all directions in a fluid), and acts on the boundary of an object. Stress is an internal reaction within the material, can be tensile, compressive, or shear, is a tensor quantity (varies with direction and plane), and exists throughout the volume of the material. In engineering, pressure refers to fluid/gas forces on surfaces, while stress refers to the material's internal response to all applied loads.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy