What next?
Modulus comes from stress over strain. These are its inputs and uses.
How to use this calculator
- Enter the stress (σ) in megapascals.
- Enter the strain (ε) as a decimal ratio.
- Read the Young’s modulus in gigapascals.
What your result means
Young's modulus measures stiffness — how much stress it takes to stretch a material by a given strain. A high modulus (like steel at ~200 GPa) means the material barely deforms; a low one (like rubber) stretches easily.
Why this one is different
Strain is expected as a decimal, not a percentage, and the page says so where you can see it: entering 0.2 instead of 0.002 overstates the modulus a hundredfold and is the commonest way this calculation goes wrong. A strain of zero leaves an em dash in every row rather than a fabricated zero, and the division is printed with your own figures in place.
Stiffness is a property, not a size
Young's modulus is the slope of the straight, elastic part of a stress-strain curve. It belongs to the material itself — steel is about 200 GPa whether it's a paperclip or a bridge girder — so it lets engineers predict deflection before anything is built.
How it works
Young's modulus equals stress divided by strain in the elastic region, where deformation is still reversible. Because strain is dimensionless, the modulus carries the same units as stress — pascals.
Formula
Worked example
A specimen under 50 MPa of stress showing 0.00025 strain:
E = 50 ÷ 0.00025 MPa
E = 200,000 MPa
E = 200 GPa
200 GPa is the textbook figure for structural steel. Aluminium is about 70 GPa, concrete roughly 30 GPa and timber 8–14 GPa along the grain.
Stiffness is not strength
Young’s modulus describes how much a material deflects under load within the elastic region. It says nothing about how much load the material can take before it yields or breaks — that is strength, a separate property. Cast iron is stiffer than aluminium but far more brittle; a bow is strong yet deliberately not stiff. Confusing the two leads to the wrong material choice: a deflection problem is solved with stiffness or geometry, a failure problem with strength.
Where the linear assumption ends
The modulus is the gradient of the initial straight portion of the stress–strain curve, so it is only meaningful below the proportional limit. Past that point the curve bends, the ratio stops being constant, and deformation begins to be permanent. Several common materials never have a clean linear region at all — polymers creep under sustained load, concrete is markedly non-linear in tension, and composites behave differently along and across the fibre. Take the modulus from the material’s own data at the temperature and loading rate you are working at, rather than from a textbook average.
Frequently asked questions
What units is Young’s modulus in?＋
Pascals (Pa), the same as stress. Real materials are stiff, so values are usually quoted in gigapascals (GPa) — steel is around 200 GPa, aluminium around 69 GPa.
Does it only apply in the elastic region?＋
Yes. Young’s modulus describes the linear, reversible part of the stress-strain curve. Beyond the yield point the material deforms permanently and the ratio no longer holds.
Does a higher Young’s modulus mean a stronger material?＋
No, it means a stiffer one. Young’s modulus describes how much a material deflects under load, not how much load it survives before failing. Steel at 200 GPa is roughly three times stiffer than aluminium at 70 GPa, but strength is a separate property measured by yield and ultimate stress.
What are typical values for common materials?＋
Steel is about 200 GPa, aluminium 69, concrete 30 or so, and timber along the grain roughly 10. Rubber is a few megapascals, four orders of magnitude below steel.
Is a stiff material also a strong one?＋
No, and confusing the two is the classic error. Stiffness resists deflection, strength resists failure. Cast iron is stiff and brittle; mild steel is equally stiff but far tougher.
How does this apply to choosing a beam?＋
Deflection depends on the modulus and on the section's second moment of area. Changing material moves the modulus a little, while making the section deeper moves the geometry term with the cube of depth, which is usually the far cheaper lever.
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Assumptions & limitations
Engineering formulas are exact; the situations they model are not. Read your result with these limits in mind:
- Young's modulus is defined only for the linear-elastic part of the stress-strain curve, before yield.
- Assumes the material is isotropic — the same stiffness in every direction. Timber, composites and rolled metals are not.
- Temperature changes stiffness: most metals lose modulus as they heat, and polymers change dramatically near their glass transition.
- Stiffness (E) is not strength. A stiff material can still be brittle, and a strong material can be relatively flexible.