Stress and Strain Calculator
When a force is applied to a solid material, two things happen simultaneously: the material develops an internal resistance to the force, which is called stress, and it changes shape slightly, which is called strain. Understanding the relationship between stress and strain is fundamental to selecting and designing structural components, from steel bolts and concrete columns to plastic housings and rubber gaskets. Engineering stress is defined as the force per unit of original cross-sectional area. The SI unit is the pascal, but in practice megapascals (MPa, or newtons per square millimetre) are used for most structural materials. Engineering strain is the change in length divided by the original length, a dimensionless ratio. For most metals and engineering plastics in the elastic range, stress and strain are proportional: doubling the stress doubles the strain. The constant of proportionality is called Young's modulus or the elastic modulus, symbolised E. This calculator lets you enter the applied force in newtons, the cross-sectional area in square metres, the original length in metres, and the extension (change in length) in millimetres. It returns the stress in megapascals, the strain as a dimensionless number (and in scientific notation), and the Young's modulus in gigapascals. You can use it to characterise a material from a tensile test result, to predict elongation under a known load, or to cross-check a published modulus value. Results are for the linear elastic regime and assume a uniform cross-section under axial load.
How it works
Engineering stress: sigma = F / A in pascals; divide by 10 to the 6 for MPa. Engineering strain: epsilon = (delta-L / 1000) / L (delta-L is entered in mm, converted to m by dividing by 1000). Young's modulus: E = sigma (Pa) / epsilon; divide by 10 to the 9 for GPa. These are standard elastic (Hooke's law) relationships valid in the linear portion of a stress-strain curve, before yielding.
Worked example
A bar is loaded with F = 10,000 N and has a cross-sectional area A = 0.001 m². Stress = 10000 / 0.001 = 10,000,000 Pa = 10.00 MPa. The bar has an original length L = 1 m and stretches by delta-L = 0.5 mm = 0.0005 m. Strain = 0.0005 / 1 = 5.00 × 10-4 (written as 0.0005 or 5e-4). Young's modulus = 10,000,000 / 0.0005 = 20,000,000,000 Pa = 20.00 GPa. This value is lower than steel (200 GPa), suggesting this could be a polymer or softer alloy.
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