---
title: "Stress, Strain and the Young Modulus"
description: "Dividing force by cross-sectional area and extension by original length removes the size of the sample, leaving numbers that describe the material itself. The gradient of the straight part of a stress"
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: 2026-09-12
---

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# Stress, Strain and the Young Modulus

Dividing force by cross-sectional area and extension by original length removes the size of the sample, leaving numbers that describe the material itself. The gradient of the straight part of a stress-strain graph is the Young modulus.

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

Pull a wire and two numbers tell the story. Stress is force over cross section, in pascals. Strain is extension over original length, with no units at all. For small pulls they grow in proportion, and big stress with tiny strain means a stiff sample.

The gradient of the straight part of a stress against strain graph is the Young modulus. Its unit is the pascal, and steel scores far above rubber. Work well below the yield point, with a safety factor, to keep bridges and cables alive.

A thin wire and a thick rod of the same metal share one modulus. Doubling the area halves the stress, but the strain follows suit and the ratio stays fixed. Geometry sets the extension, while the material sets the modulus.

**Recap.** Divide out the size to get stress and strain, read stiffness off the gradient, and trust it for every shape.

## 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)
- [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)