Young's Modulus Calculator
Young's modulus from one stress–strain point (secant) or a least-squares slope over several points, with decimal, percent or microstrain input.
Inputs
Young's modulus from one stress–strain point (secant) or a fitted slope over several points, with explicit strain units.
Enter the values and press Calculate.
Or load an example to see a worked result.
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- For one test point, enter the stress (or force and original area) and the strain (or original gauge length and extension). Say whether strain is a decimal, a percentage or microstrain.
- For several points, switch to “Several points”, paste one “strain, stress” pair per line from the straight part of your curve, and optionally limit the fit to a strain interval.
- Read E — labelled as a single-point secant value or a fitted slope — with the working, and for a fit the intercept, R² and residuals.
How it works
Stress σ = F ÷ A (N ÷ mm² = MPa) and strain ε = ΔL ÷ L0. Percent strain is divided by 100; microstrain multiplied by 10⁻⁶. One point gives the secant modulus through the origin, E = σ ÷ ε.
Several points give the least-squares slope E = Σ(ε − ε̄)(σ − σ̄) ÷ Σ(ε − ε̄)², with the intercept and fitted strain range shown, so a seating offset at the start of a test does not bias E.
Zero strain is refused, and stress and strain of opposite signs are flagged. The value is an apparent stiffness that includes machine compliance unless strain was measured on the specimen. No yield point is detected and no material grade is certified.
Worked example
250 MPa at 0.125 % strain. 0.125 % = 0.00125, so E = 250 MPa ÷ 0.00125 = 200,000 MPa = 200 GPa. The same strain from a 100 mm gauge length extending 0.125 mm gives the same 200 GPa, and so does 25 kN on 100 mm² (250 MPa). A zero strain has no modulus.
Frequently asked questions
Percent or decimal strain?
Either, as long as you say which. 0.125 % is 0.00125 as a decimal and 1,250 microstrain. Entering a percentage as a decimal makes E a hundred times too small — the strain unit selector prevents that.
Secant or slope?
A single point gives the secant modulus — the line from the origin to that point. A fitted slope over several points in the linear region is usually better: it averages scatter and is not thrown off by an offset at the start of the test.
Can I use post-yield points?
Not for Young's modulus. E describes the straight elastic part only; points past the proportional limit flatten the slope. Use the fit interval to keep only the elastic points — the tool does not find the yield point for you.
Can I use these results for final design?
No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.
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Cite this tool
Zerdly. (2026). Young's Modulus Calculator. Retrieved from https://www.zerdly.com/tools/youngs-modulus-calculator/
Tip: Enter any known values to calculate the remaining results.
Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.