Young's Modulus Calculator
Find a material's stiffness from stress and strain.
Results update as you type.
How it works
Young's modulus, also called the elastic modulus, measures how stiff a material is, and this calculator finds it from a simple tension test. You enter the applied force, the cross-sectional area of the sample, its original length, and how much it stretched, and it returns Young's modulus along with the stress and strain. The concept comes from Hooke's law for materials: within the elastic range, stress is proportional to strain, and the constant of proportionality is Young's modulus. Stress is the force spread over the cross-sectional area, in pascals, while strain is the fractional change in length, a dimensionless ratio. A high modulus, like steel's roughly 200 gigapascals, means the material barely deforms under load, while a low modulus, like rubber's, means it stretches easily. Engineers use Young's modulus to predict how much a component will deflect under load, to select materials for stiffness, and to design everything from beams and bridges to springs and biomedical implants. The value is a material property independent of the object's size, since stress and strain already normalize for area and length. This calculation assumes the material is in its linear elastic region, before any permanent deformation. Enter the force, area, length, and extension to compute Young's modulus.
E = stress / strain = (F/A) / (ΔL/L)
Young's modulus is the ratio of stress to strain in the elastic region of a material. Stress is the applied force divided by the cross-sectional area, and strain is the extension divided by the original length. Dividing stress by strain gives the modulus in pascals, a measure of stiffness: higher values mean a stiffer material that deforms less under load.
Source:Materials science
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Worked example
How to use this calculator
- 1
Enter your values
Enter applied force, cross-sectional area, original length and extension.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Young's modulus updates instantly as you type — no button to press.
Frequently asked questions
What is Young's modulus?
Young's modulus, or the elastic modulus, is a measure of a material's stiffness, defined as the ratio of stress to strain in the elastic region. A higher modulus means the material resists deformation more strongly. It is a fundamental material property used throughout engineering to predict how components respond to loads.
How is Young's modulus calculated?
Divide the stress by the strain. Stress is the applied force divided by the cross-sectional area, and strain is the extension divided by the original length. So the modulus equals force times length divided by area times extension. The calculator computes stress, strain, and the modulus from your four inputs automatically.
What are typical Young's modulus values?
Values vary enormously by material. Steel is around 200 gigapascals, aluminum about 70, concrete roughly 30, wood a few gigapascals, and rubber only a few megapascals. A higher value means a stiffer material. Comparing moduli helps engineers choose materials that provide the required stiffness for a given application.
What is the difference between stress and strain?
Stress is the internal force per unit area within a material, measured in pascals, caused by an external load. Strain is the resulting deformation expressed as the fractional change in length, which is dimensionless. Young's modulus links the two: it is the stress needed to produce a given strain in the elastic range.
Does this apply beyond the elastic limit?
No. Young's modulus describes behavior only in the linear elastic region, where the material returns to its original shape after the load is removed and stress is proportional to strain. Beyond the elastic limit, the material deforms permanently and the stress-strain relationship becomes nonlinear, so the simple modulus formula no longer applies.