# Young's Modulus: Definition & Equations

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• 0:05 Definition of Young's Modulus
• 1:05 Stress Versus Strain
• 2:16 Elasticity of a Material
• 3:31 Practice for Using…
• 4:50 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Young's modulus is a material property that tells you how stiff or stretchy a material is. In this lesson, learn how to calculate Young's modulus and what it can tell you about the material.

## Definition of Young's Modulus

Imagine that you pull a rubber band. It stretches a lot, right? Now, what would happen if you pulled on a piece of copper wire with the same force? Would it stretch as much as the rubber band? Probably not, because we all know that copper is a much stiffer material than rubber.

Even though we know that rubber is more elastic and stretchy than copper, we need a way to measure and quantify exactly how stretchy or stiff a material is. The Young's modulus of a material is a number that tells you exactly how stretchy or stiff a material is, a property known as elasticity.

Materials like rubber have a very low Young's modulus, which means that they stretch a lot when you apply even a small force to them. Other materials, including metals like copper, are much stiffer and have a higher Young's modulus. They can still stretch if you apply a big enough force, but it takes a lot more force to stretch copper than a rubber band. Some materials, such as hard ceramics and diamonds, are even stiffer than metals and have an even higher Young's modulus.

## Stress Versus Strain

Before you can learn how to calculate the Young's modulus of a material, you need to know something about two other important measurements: stress and strain.

Stress measures the force per unit area applied to an object. To find stress, divide the amount of force applied to the object by the cross-sectional area of the object you are applying the force to. The units used to measure stress are the same used to measure pressure, Pascals (or Pa).

Cross-sectional area means the area of a slice right through the middle of the object. Most of the time, when you are testing a material to find the stress, the cross-section will either be a circle or a square, and you can find the area using simple geometry.

Strain measures how much an object stretches relative to its original length. To find the strain, divide the change in length after you apply the force by the original length. Strain is a unitless number because the units of the numerator and denominator are the same, so when you divide them, there are no units in the result. The reason that you divide by the original length (to find strain) or area (to find stress) is so you can find quantities that are entirely dependent on the type of material and not on the size of the object.

## Elasticity of a Material

The elasticity of a material measures how stiff or stretchy it is. You can think of it as how much strain a material exhibits in response to stress. One way to determine a material's elasticity is to calculate a quantity called Young's modulus (symbol: E or Y), which is also sometimes known as the elastic modulus.

To find the Young's modulus of a material, simply divide the stress by the strain:

Young's modulus is a great way to tell how elastic a material is. Very elastic materials, like rubber bands, will have a relatively small Young's modulus because they exhibit a high strain in response to a relatively low stress. A typical Young's modulus value for rubber is 0.01 GPa. Please note that 1 GPa = 109 Pa.

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