Young's Modulus Calculator
Calculate Young's modulus from stress and strain, or from force, area, and length change. Useful for estimating material stiffness.
Young's Modulus Calculator
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What the Young's modulus calculator does
Young's modulus measures how stiff a material is, how strongly it resists being stretched. This calculator finds it two ways: directly from a known stress and strain, or from the raw measurements of force, area, and the change in length under load, working out the stress and strain along the way.
Below is what Young's modulus means, the equations behind it, why stiffness is different from strength, and a worked example.
How to use it
- Choose a method: from stress and strain directly, or from force, area, and the initial and final length.
- Enter the values the method asks for.
- Press Calculate for Young's modulus, along with the stress and strain when you use the second method, or Reset to clear it.
What Young's modulus measures
Young's modulus is a material's stiffness in tension, how much stress it takes to stretch it by a given fraction. Pull on a steel bar and it barely lengthens; pull on a rubber band of the same size with the same force and it stretches enormously. Steel has a high Young's modulus and rubber a low one, and the modulus puts a precise number to that difference.
It is a property of the material itself, not of the particular object. A thick steel beam and a thin steel wire have the same Young's modulus, even though the wire stretches more under the same force, because the modulus compares stress to strain rather than force to length. That makes it one of the most useful numbers in engineering, fixed for each material and listed in every reference table.
The equations it uses
Young's modulus E is the ratio of stress to strain:
E = σ ÷ ε
When you supply force, area, and lengths instead, the calculator first builds the stress and strain from them, the stress as force over area and the strain as the change in length over the original length:
σ = F ÷ A and ε = ΔL ÷ L0
then divides one by the other. Because strain is a pure number, Young's modulus comes out in the same units as stress, pascals.
Stiffness, not strength
It is worth being clear that Young's modulus measures stiffness, which is not the same as strength. Stiffness is how much a material resists stretching; strength is how much stress it can take before it yields or breaks. A material can be very stiff yet not especially strong, or strong yet flexible, so the two properties describe different things.
Young's modulus also applies only while a material behaves elastically, springing back when the load is removed. In that range, stress and strain rise in proportion and their ratio holds steady, which is what makes the modulus a fixed number. Push a material past its elastic limit and it starts to deform permanently, the simple proportion breaks down, and Young's modulus no longer describes what happens. Within safe, elastic loads, though, it reliably predicts how much a part will stretch.
Units and precision
The calculator works in SI units: force in newtons, area in square metres, length in metres, stress and Young's modulus in pascals, and strain as a pure number. Because materials are stiff, Young's modulus values are large, usually quoted in gigapascals, billions of pascals, such as around 200 for steel or 70 for aluminium. Results are carried to several figures, finer than material data is usually known.
A worked example: steel
Suppose a steel sample is under a stress of 100 MPa and is measured to have a strain of 0.0005, that is, it stretched by one part in two thousand.
Young's modulus is E = 100,000,000 ÷ 0.0005 = 200,000,000,000 Pa, or 200 GPa. That is the standard stiffness of steel, which is why a strain of only 0.0005 needs as much as 100 MPa of stress to produce it: steel is stiff, and resists stretching hard.
Questions people ask
What is the formula for Young's modulus?
It is stress divided by strain, E = σ/ε. From raw measurements, it is the force over area divided by the fractional change in length.
Does Young's modulus measure strength?
No, it measures stiffness, the resistance to stretching. Strength is the stress a material can take before failing, which is a separate property; a stiff material is not necessarily a strong one.
What are the units of Young's modulus?
The same as stress, pascals, because strain has no units. Material values are large, so gigapascals (GPa) are usual, like 200 GPa for steel.
What are some typical values?
Roughly 200 GPa for steel, 70 GPa for aluminium, around 10 to 15 GPa for wood along the grain, and well under 1 GPa for rubber, which is why rubber stretches so easily.
References
A quick note on where the physics comes from. Young's modulus as the ratio of stress to strain in the elastic range is standard mechanics of materials, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The pascal and the other SI units follow the US National Institute of Standards and Technology.
- OpenStax, University Physics Volume 1, Section 12.3, Stress, Strain, and Elastic Modulus. https://openstax.org/books/university-physics-volume-1/pages/12-3-stress-strain-and-elastic-modulus
- HyperPhysics, Georgia State University, Elastic Modulus, Young's Modulus. http://hyperphysics.phy-astr.gsu.edu/hbase/permot.html
- National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811
Bibek Lal Karna is a PhD student and graduate teaching assistant at the University of Mississippi, with deep interests in theoretical and gravitational physics. He is also the founder of NRCC and is strongly engaged in scientific teaching and communication. At Eon Tools, he reviews physics tools.