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| Material | Typical E (GPa) | Force | Area | Length | Deformation |
|---|---|---|---|---|---|
| Steel (carbon) | 190–210 | 500 N | 10 mm² | 200 mm | 0.20 mm |
| Aluminum (6061) | 68–70 | 400 N | 20 mm² | 250 mm | 0.71 mm |
| Brass | 90–110 | 600 N | 15 mm² | 300 mm | 1.21 mm |
Young’s modulus relates axial stress to axial strain within the linear elastic region:
E = σ / ε
With:
Combining both gives the practical estimator:
E = (F · L) / (A · ΔL)
Young’s modulus (E) describes how strongly a material resists elastic stretching or compression. In the linear region of a stress–strain curve, E is the slope: a steeper slope means higher stiffness. Because E compares stress to strain, it is independent of specimen geometry when measurements are taken correctly.
Engineering metals commonly range from about 60–220 GPa. Aluminum alloys sit near 69 GPa, copper alloys near 100–130 GPa, and carbon steels around 190–210 GPa. Concrete is much lower (roughly 20–40 GPa), while polymers can fall below 5 GPa depending on formulation and temperature. Ceramics vary widely, often 100–400 GPa, but fracture at low strain, so measurements usually use very small elastic extensions.
Force, area, gauge length, and extension must be consistent and well measured. Small errors in deformation are amplified because strain uses ΔL/L. For stiff materials, ΔL can be tiny, so use an extensometer or a displacement sensor with appropriate resolution. Measure diameter or width at several points and average, since a 1% area error produces a 1% stress error.
Stress (σ) equals force divided by area, reported in pascals (Pa). Strain (ε) is dimensionless, the ratio of deformation to original length. Reporting strain as a percentage can help spot unrealistic inputs; many elastic tests use strains well below 1%.
This estimator assumes the test point lies within the elastic region where Hooke’s law holds. If the specimen has yielded, cracked, or undergone viscoelastic creep, the calculated E no longer represents a true elastic modulus and may appear artificially low.
Metals often show modest modulus changes with temperature, while polymers can change dramatically near glass-transition. Loading rate and time under load also affect viscoelastic materials, so compare results only under similar conditions.
Designers use E to estimate deflection, vibration response, and load sharing in assemblies. For beams and columns, modulus couples with geometry (moment of inertia) to control stiffness. Selecting materials with a higher E typically reduces deflection without increasing cross-section.
Run several trials, verify units, and review the displayed stress and strain for sanity. Save each calculation to build a small dataset, then export CSV for spreadsheets or PDF for lab notes. For reporting, state the test setup, gauge length, and measurement method.
It is measured in pascals (Pa), equivalent to newtons per square meter. In engineering, values are often reported in gigapascals (GPa) for metals and megapascals (MPa) for softer materials.
Check area and deformation units first. Using mm² as m² or mm as m will inflate stiffness dramatically. Also ensure the deformation is the elastic extension at the given force, not total machine travel.
The specimen may be beyond the linear elastic range, slipping in grips, or experiencing creep. Large strains or cracking reduce apparent modulus. Confirm the point is elastic and that extension is measured on the gauge length.
Yes. The same formulas apply for axial compression if deformation is measured accurately and buckling is avoided. For slender samples, buckling can dominate and corrupt the modulus estimate.
At least three is common for a quick estimate. For lab reporting, five or more improves confidence. Export the history to compute mean, standard deviation, and identify outliers.
Ideally, no. E is a material property. In practice, poor area measurement, non-uniform cross-sections, or inaccurate gauge length can make results appear size-dependent.
Use higher-resolution measurement. For stiff materials, small ΔL can be near instrument noise, causing unstable results. Increase gauge length, use an extensometer, or average multiple readings at nearby load points.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.