--- title: "Stress, Strain and the Young Modulus" description: "Stress is axial force divided by cross-sectional area. Strain is extension divided by original length. In the linear elastic region, the gradient of stress against strain gives the Young modulus, a ma" canonical: https://lightmysky.com/learn/science/stress-strain-and-the-young-modulus-mt_uWdqhWGT7Y source: https://lightmysky.com/learn/science/stress-strain-and-the-young-modulus-mt_uWdqhWGT7Y.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Stress, Strain and the Young Modulus Stress is axial force divided by cross-sectional area. Strain is extension divided by original length. In the linear elastic region, the gradient of stress against strain gives the Young modulus, a material property under stated test conditions. Subject: Science · Area: Matter & Materials · Ages 17 to 18 Page: https://lightmysky.com/learn/science/stress-strain-and-the-young-modulus-mt_uWdqhWGT7Y ## Ready when they can - Calculates stress in pascals and strain as a ratio for a wire under a stated load - Finds the Young modulus as a gradient and quotes it with its unit - Explains why two wires of the same material but different thickness give the same modulus ## Lesson: Stress, strain, and true stiffness You have compared force and extension. For a uniform wire pulled along its length, tensile stress = force / cross-sectional area. Use newtons and square metres to get pascals: 1 Pa = 1 N/m squared. For circular diameter d, area = pi × (d/2) squared. Convert d to metres before squaring; 1 mm = 0.001 m. Use the wire's tension, not the sum of the opposite end forces. Tensile strain = extension / original length. Extension is loaded length minus original length. Use matching length units so they cancel. A 1.5 m wire extending by 0.003 m has strain 0.003 / 1.5 = 0.002, with no units. Strain is the fractional increase in length, not the extension itself. *(drawing: Stress in MPa at two strains. Doubling strain doubles stress here. These bars are not a stress-strain graph.)* In the linear elastic region through the origin, Young modulus Y = stress / strain = (force/area) / (extension/original length). Plot stress vertically and strain horizontally. Y is the gradient: change in stress / change in strain. Its unit is Pa because strain has no units. For the bars, 100 MPa / 0.001 = 100000000000 Pa. A larger Y means less strain at the same stress. Compare wires of the same material, processing and direction at the same temperature. In the linear elastic region, Y does not depend on length or area. At fixed force, doubling area halves stress and strain, leaving their ratio unchanged. A sample's force-extension stiffness still depends on its dimensions. The material modulus and the sample's stiffness are different quantities. Elastic deformation disappears after unloading. The proportionality limit ends the straight-line region; the elastic limit marks the onset of permanent deformation. A curved region can still be elastic. Do not use one constant stress/strain ratio outside the linear region. Working below yield with a suitable safety factor reduces the risk of permanent deformation. Young modulus alone cannot establish a safe working load. **Recap.** Stress = force/area. Strain = extension/original length. Their ratio gives Young modulus in the linear elastic region, in pascals. *Lesson, questions and flashcards written for this dataset. Mechanics references were consulted for facts and calculation methods.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Elastic Strain Energy and Force-Extension Graphs](https://lightmysky.com/learn/science/elastic-strain-energy-and-force-extension-graphs-mt_4WnFUmR13O) ## Optional connections - [Density and How to Measure It](https://lightmysky.com/learn/science/density-and-how-to-measure-it-mt_HrKI1-UzfI) ## Opens up - [Bone, Cartilage and the Mechanics of a Joint](https://lightmysky.com/learn/science/bone-cartilage-and-the-mechanics-of-a-joint-mt_1_q3aL7E5D) - [Circular Motion: Angular Speed and Centripetal Force](https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq)