Young's Modulus
Stiffness of a material (stress over strain).
Formula
Variables
Example
Steel’s Young’s modulus (~200 GPa) is why it barely stretches under load.
How it works
Young’s modulus tells you how much a material resists being elastically stretched or compressed. It is defined as stress divided by strain because stress measures the internal force spread over area, while strain measures the resulting fractional change in length, so their ratio captures how much load is needed to produce a given proportional deformation. A higher value means the material is stiffer and changes shape less for the same applied stress.
When to use it
Use this formula when you want to estimate elastic deformation in rods, beams, wires, or other solid components before they permanently deform. It is also useful in material selection, structural design, and comparing stiffness between different materials.
Worked example, step by step
A brass rod experiences a tensile stress of 120 MPa and a strain of 0.00080. Step 1: Write the formula: E = σ / ε Step 2: Substitute the values: E = 120 MPa / 0.00080 Step 3: Calculate: E = 150,000 MPa Step 4: Convert to GPa: E = 150 GPa Final answer: The Young’s modulus of the brass rod is 150 GPa.
Common mistakes to avoid
- Using force instead of stress, or forgetting to divide force by cross-sectional area first
- Treating strain as a percentage without converting it to a decimal
- Using the formula after the material has yielded, when the stress-strain relationship is no longer linear
Did You Know?
Young's modulus measures stiffness — diamond's is about 1,000 times that of rubber.
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